02_2_test_linear_linear

Load

Estimation

Plot

linear-demand linear-cost, \(\sigma = 1\)

\(\theta = 0.05\)

\(\alpha_2 = 0.1\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.817	1.000	7.959	9.580	15.288
alpha1_hat	100	0	0.825	0.857	−1.470	0.766	3.413
alpha2_hat	100	0	0.110	0.081	−0.105	0.109	0.348
alpha3_hat	100	0	0.979	0.217	0.494	0.962	1.691
gamma0_hat	100	0	0.885	2.320	−17.279	1.197	4.363
gamma1_hat	100	0	2.497	9.899	−12.773	1.136	70.757
gamma2_hat	100	0	1.011	0.233	0.530	0.988	2.311
gamma3_hat	100	0	1.030	0.317	0.651	0.997	3.438
theta_hat	100	0	−0.808	5.535	−41.122	−0.060	9.001
theta_hat_t_stats	100	0	−0.107	1.107	−3.315	−0.044	2.587
R2_demand	100	0	0.370	0.292	−1.623	0.433	0.715
R2_supply	100	0	0.276	0.775	−6.837	0.411	0.734

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.978	0.748	8.375	9.847	12.592
alpha1_hat	100	0	0.829	0.670	−0.830	0.745	2.707
alpha2_hat	100	0	0.116	0.061	−0.056	0.113	0.304
alpha3_hat	100	0	0.999	0.167	0.570	0.990	1.613
gamma0_hat	100	0	0.845	1.132	−2.634	0.791	2.968
gamma1_hat	100	0	0.865	1.887	−8.034	1.090	4.744
gamma2_hat	100	0	1.017	0.171	0.664	1.012	1.493
gamma3_hat	100	0	1.018	0.162	0.711	0.988	1.407
theta_hat	100	0	0.147	0.959	−2.028	0.059	4.702
theta_hat_t_stats	100	0	0.081	0.930	−1.825	0.123	2.907
R2_demand	100	0	0.325	0.241	−0.787	0.387	0.644
R2_supply	100	0	0.305	0.176	−0.385	0.332	0.544

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.973	0.410	9.143	9.948	10.873
alpha1_hat	100	0	0.947	0.358	0.030	0.932	1.842
alpha2_hat	100	0	0.104	0.034	0.028	0.103	0.204
alpha3_hat	100	0	0.998	0.103	0.757	0.985	1.293
gamma0_hat	100	0	0.853	0.751	−0.897	0.999	2.610
gamma1_hat	100	0	1.016	0.984	−3.260	0.931	3.577
gamma2_hat	100	0	1.011	0.107	0.780	1.008	1.251
gamma3_hat	100	0	1.021	0.103	0.828	1.003	1.332
theta_hat	100	0	0.067	0.499	−1.557	0.102	2.117
theta_hat_t_stats	100	0	0.162	1.034	−2.557	0.317	2.408
R2_demand	100	0	0.332	0.127	−0.047	0.341	0.540
R2_supply	100	0	0.308	0.134	−0.184	0.324	0.572

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.997	0.199	9.646	9.993	10.439
alpha1_hat	100	0	0.995	0.169	0.621	0.983	1.359
alpha2_hat	100	0	0.101	0.018	0.067	0.101	0.140
alpha3_hat	100	0	1.001	0.046	0.901	0.994	1.106
gamma0_hat	100	0	0.980	0.319	0.045	1.018	1.729
gamma1_hat	100	0	1.032	0.315	0.194	1.014	1.988
gamma2_hat	100	0	1.003	0.051	0.889	0.997	1.152
gamma3_hat	100	0	1.003	0.042	0.875	1.003	1.110
theta_hat	100	0	0.037	0.165	−0.484	0.047	0.487
theta_hat_t_stats	100	0	0.202	0.947	−2.282	0.293	2.470
R2_demand	100	0	0.342	0.050	0.237	0.340	0.458
R2_supply	100	0	0.336	0.053	0.213	0.336	0.456

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.996	0.146	9.640	9.993	10.428
alpha1_hat	100	0	1.012	0.118	0.683	1.016	1.274
alpha2_hat	100	0	0.099	0.011	0.073	0.099	0.124
alpha3_hat	100	0	1.000	0.037	0.909	1.002	1.081
gamma0_hat	100	0	1.037	0.203	0.572	1.049	1.469
gamma1_hat	100	0	0.997	0.244	0.376	1.000	1.534
gamma2_hat	100	0	0.996	0.031	0.926	0.994	1.078
gamma3_hat	100	0	1.000	0.026	0.931	1.000	1.060
theta_hat	100	0	0.046	0.130	−0.225	0.042	0.325
theta_hat_t_stats	100	0	0.384	1.082	−2.184	0.370	2.702
R2_demand	100	0	0.332	0.041	0.221	0.332	0.431
R2_supply	100	0	0.338	0.034	0.261	0.341	0.414

\(\alpha_2 = 0.5\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.059	1.165	7.650	9.738	14.910
alpha1_hat	100	0	1.176	1.935	−3.982	1.278	7.462
alpha2_hat	100	0	0.490	0.207	0.124	0.465	1.534
alpha3_hat	100	0	0.985	0.246	0.477	0.942	1.737
gamma0_hat	100	0	0.729	1.769	−8.802	0.906	3.573
gamma1_hat	100	0	0.810	3.272	−5.914	0.868	15.210
gamma2_hat	100	0	1.029	0.261	0.555	1.012	2.072
gamma3_hat	100	0	1.049	0.268	0.410	0.999	2.476
theta_hat	100	0	0.129	0.535	−1.646	0.127	1.327
theta_hat_t_stats	100	0	0.167	1.045	−3.056	0.318	2.177
R2_demand	100	0	0.458	0.301	−1.023	0.537	0.783
R2_supply	100	0	0.493	0.224	−0.832	0.528	0.854

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.954	0.651	8.636	9.896	11.753
alpha1_hat	100	0	1.072	1.230	−1.860	1.047	3.562
alpha2_hat	100	0	0.486	0.131	0.170	0.479	0.855
alpha3_hat	100	0	1.000	0.157	0.639	0.996	1.408
gamma0_hat	100	0	0.845	0.956	−1.477	0.926	2.493
gamma1_hat	100	0	0.945	1.557	−2.514	0.754	6.600
gamma2_hat	100	0	1.022	0.139	0.782	1.020	1.473
gamma3_hat	100	0	1.019	0.148	0.639	1.030	1.404
theta_hat	100	0	0.080	0.275	−1.013	0.106	0.552
theta_hat_t_stats	100	0	0.202	0.932	−2.695	0.400	2.030
R2_demand	100	0	0.513	0.142	0.085	0.535	0.744
R2_supply	100	0	0.509	0.118	0.191	0.521	0.762

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.044	0.566	8.881	10.032	11.537
alpha1_hat	100	0	1.174	1.117	−1.140	0.994	4.438
alpha2_hat	100	0	0.489	0.121	0.227	0.496	0.754
alpha3_hat	100	0	1.002	0.118	0.800	0.995	1.399
gamma0_hat	100	0	0.951	0.752	−1.084	0.967	2.826
gamma1_hat	100	0	1.059	1.226	−1.989	1.206	3.678
gamma2_hat	100	0	1.007	0.111	0.782	1.002	1.320
gamma3_hat	100	0	1.009	0.113	0.724	1.006	1.378
theta_hat	100	0	0.057	0.214	−0.394	0.017	0.707
theta_hat_t_stats	100	0	0.217	0.940	−2.144	0.093	2.636
R2_demand	100	0	0.510	0.116	0.133	0.530	0.706
R2_supply	100	0	0.519	0.085	0.281	0.531	0.691

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.016	0.175	9.584	10.020	10.482
alpha1_hat	100	0	1.003	0.360	0.058	0.995	1.761
alpha2_hat	100	0	0.501	0.041	0.418	0.497	0.596
alpha3_hat	100	0	1.004	0.044	0.928	1.001	1.117
gamma0_hat	100	0	0.993	0.262	0.376	0.990	1.768
gamma1_hat	100	0	1.031	0.453	0.014	1.033	2.079
gamma2_hat	100	0	0.999	0.041	0.880	1.001	1.117
gamma3_hat	100	0	0.996	0.043	0.879	0.996	1.117
theta_hat	100	0	0.046	0.085	−0.204	0.040	0.230
theta_hat_t_stats	100	0	0.519	0.985	−2.292	0.472	2.589
R2_demand	100	0	0.519	0.039	0.418	0.519	0.600
R2_supply	100	0	0.521	0.033	0.447	0.523	0.582

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.012	0.137	9.681	9.998	10.394
alpha1_hat	100	0	0.991	0.228	0.396	1.004	1.556
alpha2_hat	100	0	0.503	0.027	0.432	0.503	0.568
alpha3_hat	100	0	1.005	0.031	0.929	1.009	1.097
gamma0_hat	100	0	1.005	0.227	0.326	0.996	1.614
gamma1_hat	100	0	0.981	0.357	0.213	1.023	1.822
gamma2_hat	100	0	1.000	0.036	0.923	1.002	1.124
gamma3_hat	100	0	0.999	0.034	0.928	0.996	1.094
theta_hat	100	0	0.051	0.064	−0.082	0.047	0.204
theta_hat_t_stats	100	0	0.854	1.063	−1.409	0.789	3.143
R2_demand	100	0	0.520	0.031	0.432	0.520	0.580
R2_supply	100	0	0.525	0.026	0.453	0.527	0.574

\(\alpha_2 = 1.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.933	0.897	7.453	9.922	12.191
alpha1_hat	100	0	0.943	3.335	−7.741	1.125	8.999
alpha2_hat	100	0	0.990	0.372	−0.355	0.966	1.926
alpha3_hat	100	0	0.992	0.218	0.563	0.996	1.477
gamma0_hat	100	0	0.640	2.061	−14.446	1.015	4.087
gamma1_hat	100	0	1.554	4.534	−18.420	1.443	16.969
gamma2_hat	100	0	1.059	0.302	0.575	1.000	3.281
gamma3_hat	100	0	1.069	0.261	0.610	1.043	2.256
theta_hat	100	0	0.052	0.626	−2.284	0.004	2.942
theta_hat_t_stats	100	0	−0.081	1.062	−2.654	0.020	1.924
R2_demand	100	0	0.599	0.163	−0.154	0.641	0.834
R2_supply	100	0	0.526	0.390	−2.942	0.590	0.827

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.938	0.640	8.767	9.912	11.649
alpha1_hat	100	0	1.277	2.296	−3.572	1.307	9.090
alpha2_hat	100	0	0.957	0.243	0.171	0.962	1.500
alpha3_hat	100	0	0.996	0.141	0.591	0.976	1.348
gamma0_hat	100	0	0.750	1.261	−4.133	0.881	3.111
gamma1_hat	100	0	0.659	2.761	−10.647	0.663	7.674
gamma2_hat	100	0	1.029	0.177	0.625	1.014	1.746
gamma3_hat	100	0	1.012	0.174	0.624	0.990	1.609
theta_hat	100	0	0.116	0.303	−0.539	0.074	1.304
theta_hat_t_stats	100	0	0.282	0.945	−1.705	0.294	2.841
R2_demand	100	0	0.562	0.128	0.062	0.583	0.757
R2_supply	100	0	0.543	0.141	0.048	0.556	0.810

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.007	0.499	8.849	9.898	12.162
alpha1_hat	100	0	1.156	1.481	−2.597	1.140	5.041
alpha2_hat	100	0	0.986	0.184	0.567	0.987	1.489
alpha3_hat	100	0	0.997	0.102	0.805	0.980	1.371
gamma0_hat	100	0	0.951	0.702	−0.596	0.977	2.583
gamma1_hat	100	0	1.142	1.640	−3.068	1.222	5.098
gamma2_hat	100	0	1.012	0.100	0.806	1.008	1.282
gamma3_hat	100	0	1.010	0.102	0.796	1.011	1.316
theta_hat	100	0	0.039	0.159	−0.323	0.032	0.481
theta_hat_t_stats	100	0	0.207	0.903	−1.874	0.217	2.135
R2_demand	100	0	0.570	0.128	−0.289	0.581	0.734
R2_supply	100	0	0.575	0.078	0.370	0.579	0.739

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.006	0.190	9.664	10.007	10.476
alpha1_hat	100	0	1.074	0.713	−0.916	1.075	3.064
alpha2_hat	100	0	0.994	0.084	0.760	0.989	1.234
alpha3_hat	100	0	0.998	0.048	0.896	0.995	1.125
gamma0_hat	100	0	1.022	0.287	0.150	1.027	1.582
gamma1_hat	100	0	0.969	0.670	−1.149	1.006	2.646
gamma2_hat	100	0	0.996	0.043	0.874	0.992	1.111
gamma3_hat	100	0	1.009	0.040	0.916	1.009	1.120
theta_hat	100	0	0.052	0.072	−0.154	0.052	0.304
theta_hat_t_stats	100	0	0.666	0.959	−2.192	0.690	3.611
R2_demand	100	0	0.570	0.032	0.490	0.574	0.662
R2_supply	100	0	0.578	0.036	0.493	0.578	0.655

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.010	0.126	9.731	9.995	10.335
alpha1_hat	100	0	1.019	0.463	0.015	1.021	2.032
alpha2_hat	100	0	1.000	0.053	0.850	1.000	1.129
alpha3_hat	100	0	1.003	0.031	0.938	1.005	1.062
gamma0_hat	100	0	0.988	0.220	0.492	0.992	1.562
gamma1_hat	100	0	0.960	0.521	−0.133	0.954	2.213
gamma2_hat	100	0	1.003	0.032	0.919	1.006	1.068
gamma3_hat	100	0	0.998	0.029	0.913	0.995	1.085
theta_hat	100	0	0.054	0.049	−0.057	0.050	0.160
theta_hat_t_stats	100	0	1.018	0.926	−1.117	0.947	3.062
R2_demand	100	0	0.571	0.024	0.493	0.572	0.614
R2_supply	100	0	0.573	0.025	0.491	0.574	0.617

\(\alpha_2 = 5.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.027	0.973	8.184	9.967	14.140
alpha1_hat	100	0	2.793	15.115	−34.879	2.222	36.412
alpha2_hat	100	0	4.848	1.764	1.841	4.817	9.933
alpha3_hat	100	0	1.004	0.222	0.481	0.970	1.743
gamma0_hat	100	0	0.904	1.700	−4.256	1.140	3.702
gamma1_hat	100	0	3.342	16.518	−32.573	3.749	46.579
gamma2_hat	100	0	0.987	0.221	0.530	0.970	1.602
gamma3_hat	100	0	1.025	0.255	0.477	1.000	2.254
theta_hat	100	0	0.035	0.415	−0.927	−0.009	1.357
theta_hat_t_stats	100	0	−0.062	0.940	−1.957	−0.037	1.841
R2_demand	100	0	0.591	0.189	−0.415	0.620	0.827
R2_supply	100	0	0.579	0.232	−0.457	0.651	0.843

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.961	0.545	8.679	9.945	11.240
alpha1_hat	100	0	1.358	8.303	−18.125	1.695	18.536
alpha2_hat	100	0	4.939	0.965	2.676	4.963	7.482
alpha3_hat	100	0	0.994	0.134	0.628	0.996	1.392
gamma0_hat	100	0	0.870	0.891	−2.312	0.924	2.966
gamma1_hat	100	0	−1.595	10.364	−32.843	−1.492	21.853
gamma2_hat	100	0	1.018	0.133	0.716	1.011	1.456
gamma3_hat	100	0	1.023	0.151	0.691	1.036	1.395
theta_hat	100	0	0.121	0.227	−0.359	0.120	0.947
theta_hat_t_stats	100	0	0.443	0.912	−2.061	0.546	2.856
R2_demand	100	0	0.622	0.105	0.291	0.640	0.816
R2_supply	100	0	0.611	0.108	0.320	0.618	0.804

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.967	0.396	9.046	9.941	10.802
alpha1_hat	100	0	0.952	7.211	−15.549	1.057	18.070
alpha2_hat	100	0	4.972	0.807	3.013	4.915	6.846
alpha3_hat	100	0	1.001	0.099	0.769	0.993	1.269
gamma0_hat	100	0	1.000	0.728	−0.759	1.040	2.401
gamma1_hat	100	0	1.201	7.393	−16.017	0.730	22.576
gamma2_hat	100	0	0.997	0.105	0.778	0.991	1.339
gamma3_hat	100	0	1.008	0.109	0.781	0.998	1.265
theta_hat	100	0	0.052	0.179	−0.443	0.026	0.470
theta_hat_t_stats	100	0	0.214	1.078	−2.563	0.218	2.362
R2_demand	100	0	0.620	0.068	0.439	0.633	0.746
R2_supply	100	0	0.614	0.077	0.318	0.629	0.733

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.021	0.196	9.574	9.984	10.626
alpha1_hat	100	0	1.292	2.799	−5.567	0.953	9.036
alpha2_hat	100	0	4.988	0.341	4.140	4.967	5.810
alpha3_hat	100	0	1.001	0.047	0.903	1.002	1.120
gamma0_hat	100	0	1.023	0.296	0.171	1.025	1.626
gamma1_hat	100	0	0.913	3.009	−5.073	1.151	8.242
gamma2_hat	100	0	0.996	0.043	0.900	0.994	1.111
gamma3_hat	100	0	1.002	0.046	0.881	0.998	1.107
theta_hat	100	0	0.049	0.069	−0.114	0.044	0.193
theta_hat_t_stats	100	0	0.717	1.039	−1.909	0.685	2.878
R2_demand	100	0	0.617	0.036	0.502	0.619	0.691
R2_supply	100	0	0.626	0.030	0.552	0.627	0.698

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.003	0.139	9.664	9.999	10.391
alpha1_hat	100	0	0.892	1.788	−4.114	0.834	4.986
alpha2_hat	100	0	5.011	0.207	4.459	5.035	5.508
alpha3_hat	100	0	0.999	0.029	0.933	0.997	1.060
gamma0_hat	100	0	1.027	0.191	0.554	1.038	1.529
gamma1_hat	100	0	0.824	2.086	−5.515	0.945	6.108
gamma2_hat	100	0	0.998	0.028	0.927	0.999	1.073
gamma3_hat	100	0	0.997	0.032	0.924	0.995	1.068
theta_hat	100	0	0.050	0.046	−0.063	0.052	0.192
theta_hat_t_stats	100	0	1.057	0.982	−1.450	1.124	3.838
R2_demand	100	0	0.619	0.023	0.550	0.624	0.662
R2_supply	100	0	0.623	0.020	0.575	0.623	0.669

\(\alpha_2 = 20.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.078	1.156	7.657	10.040	17.632
alpha1_hat	100	0	2.394	47.415	−116.140	1.858	116.686
alpha2_hat	100	0	20.067	5.963	8.920	19.537	49.105
alpha3_hat	100	0	1.028	0.243	0.532	0.999	2.502
gamma0_hat	100	0	1.099	1.335	−5.080	1.365	3.467
gamma1_hat	100	0	11.897	57.608	−94.735	18.775	208.804
gamma2_hat	100	0	0.987	0.216	0.494	0.972	1.955
gamma3_hat	100	0	0.983	0.224	0.552	0.945	1.687
theta_hat	100	0	−0.012	0.361	−1.222	−0.025	1.432
theta_hat_t_stats	100	0	−0.133	0.987	−2.743	−0.090	1.916
R2_demand	100	0	0.564	0.537	−4.527	0.655	0.827
R2_supply	100	0	0.630	0.146	0.159	0.652	0.837

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.000	0.682	8.803	9.929	12.743
alpha1_hat	100	0	2.544	33.319	−74.863	0.205	79.604
alpha2_hat	100	0	19.850	3.830	11.814	20.057	30.398
alpha3_hat	100	0	0.992	0.157	0.692	0.984	1.611
gamma0_hat	100	0	0.911	0.894	−1.489	0.976	2.832
gamma1_hat	100	0	−0.519	40.158	−115.921	−0.394	114.922
gamma2_hat	100	0	1.021	0.138	0.680	1.028	1.385
gamma3_hat	100	0	1.006	0.140	0.695	0.998	1.461
theta_hat	100	0	0.067	0.216	−0.399	0.048	0.700
theta_hat_t_stats	100	0	0.207	0.973	−2.418	0.258	2.427
R2_demand	100	0	0.618	0.129	−0.022	0.636	0.788
R2_supply	100	0	0.630	0.104	0.224	0.646	0.817

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.994	0.371	9.163	10.035	11.065
alpha1_hat	100	0	0.532	21.853	−67.392	−0.577	48.025
alpha2_hat	100	0	20.039	2.642	13.664	20.145	27.673
alpha3_hat	100	0	0.991	0.103	0.703	1.002	1.231
gamma0_hat	100	0	0.994	0.802	−1.146	1.086	2.491
gamma1_hat	100	0	3.179	21.209	−59.636	3.509	66.693
gamma2_hat	100	0	1.008	0.110	0.778	0.990	1.279
gamma3_hat	100	0	1.004	0.107	0.793	0.991	1.428
theta_hat	100	0	0.037	0.144	−0.300	0.038	0.415
theta_hat_t_stats	100	0	0.170	0.935	−2.326	0.258	2.641
R2_demand	100	0	0.633	0.073	0.391	0.644	0.773
R2_supply	100	0	0.632	0.073	0.423	0.641	0.767

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.019	0.174	9.616	10.026	10.367
alpha1_hat	100	0	−0.831	10.322	−28.642	−1.953	26.857
alpha2_hat	100	0	20.251	1.177	16.694	20.211	23.084
alpha3_hat	100	0	1.006	0.041	0.912	1.012	1.103
gamma0_hat	100	0	0.964	0.300	0.199	0.960	1.919
gamma1_hat	100	0	−1.540	10.888	−31.544	−2.235	25.781
gamma2_hat	100	0	1.008	0.043	0.883	1.004	1.144
gamma3_hat	100	0	1.001	0.045	0.859	1.001	1.124
theta_hat	100	0	0.065	0.064	−0.073	0.064	0.204
theta_hat_t_stats	100	0	0.983	0.966	−1.289	0.993	3.082
R2_demand	100	0	0.634	0.028	0.545	0.635	0.696
R2_supply	100	0	0.631	0.031	0.539	0.633	0.692

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.999	0.137	9.610	10.001	10.327
alpha1_hat	100	0	1.356	8.204	−15.540	0.259	21.595
alpha2_hat	100	0	19.974	0.969	18.050	19.986	22.431
alpha3_hat	100	0	1.004	0.032	0.889	1.004	1.073
gamma0_hat	100	0	1.013	0.197	0.398	1.013	1.388
gamma1_hat	100	0	1.539	7.142	−15.781	1.533	22.144
gamma2_hat	100	0	1.000	0.031	0.932	0.999	1.092
gamma3_hat	100	0	0.997	0.033	0.912	0.993	1.077
theta_hat	100	0	0.045	0.041	−0.050	0.047	0.141
theta_hat_t_stats	100	0	0.983	0.887	−1.082	1.037	3.040
R2_demand	100	0	0.630	0.022	0.580	0.629	0.688
R2_supply	100	0	0.632	0.021	0.576	0.634	0.673

\(\theta = 0.1\)

\(\alpha_2 = 0.1\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.922	1.004	7.786	9.863	14.467
alpha1_hat	100	0	0.980	0.866	−0.802	0.867	3.118
alpha2_hat	100	0	0.097	0.084	−0.101	0.096	0.362
alpha3_hat	100	0	0.993	0.247	0.475	0.952	2.143
gamma0_hat	100	0	0.696	1.897	−6.221	1.122	4.230
gamma1_hat	100	0	0.268	6.858	−39.767	0.995	20.044
gamma2_hat	100	0	1.029	0.259	0.404	0.976	1.805
gamma3_hat	100	0	1.045	0.267	0.450	1.008	1.922
theta_hat	100	0	0.585	3.766	−8.145	0.146	22.392
theta_hat_t_stats	100	0	0.144	1.034	−2.194	0.184	3.212
R2_demand	100	0	0.313	0.320	−1.342	0.399	0.705
R2_supply	100	0	0.256	0.428	−2.808	0.364	0.755

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.982	0.793	8.536	9.913	14.488
alpha1_hat	100	0	0.983	0.706	−0.476	0.892	4.420
alpha2_hat	100	0	0.101	0.061	−0.055	0.101	0.364
alpha3_hat	100	0	0.998	0.183	0.695	0.974	2.060
gamma0_hat	100	0	0.951	0.981	−3.125	0.974	3.052
gamma1_hat	100	0	1.664	7.218	−18.935	1.102	56.585
gamma2_hat	100	0	1.005	0.144	0.694	1.005	1.527
gamma3_hat	100	0	1.008	0.161	0.585	0.980	1.368
theta_hat	100	0	0.002	2.669	−15.902	0.117	11.026
theta_hat_t_stats	100	0	0.215	1.044	−2.261	0.120	2.577
R2_demand	100	0	0.279	0.311	−2.128	0.345	0.582
R2_supply	100	0	0.293	0.171	−0.510	0.311	0.622

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.017	0.514	8.751	9.988	11.461
alpha1_hat	100	0	1.064	0.383	0.235	1.066	1.977
alpha2_hat	100	0	0.094	0.040	0.005	0.091	0.220
alpha3_hat	100	0	1.007	0.101	0.823	0.997	1.310
gamma0_hat	100	0	0.861	0.777	−1.152	0.850	2.406
gamma1_hat	100	0	0.916	1.588	−10.603	1.041	5.889
gamma2_hat	100	0	1.013	0.111	0.809	1.003	1.346
gamma3_hat	100	0	1.023	0.114	0.790	1.024	1.432
theta_hat	100	0	0.160	0.803	−2.355	0.113	5.796
theta_hat_t_stats	100	0	0.265	1.075	−2.432	0.237	3.224
R2_demand	100	0	0.310	0.134	−0.144	0.327	0.574
R2_supply	100	0	0.296	0.146	−0.257	0.321	0.568

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.008	0.185	9.641	10.009	10.470
alpha1_hat	100	0	0.987	0.168	0.606	0.985	1.521
alpha2_hat	100	0	0.102	0.016	0.055	0.102	0.131
alpha3_hat	100	0	0.998	0.046	0.873	0.998	1.120
gamma0_hat	100	0	0.991	0.326	0.062	1.004	1.792
gamma1_hat	100	0	1.052	0.348	0.132	1.088	1.913
gamma2_hat	100	0	0.999	0.044	0.899	0.999	1.099
gamma3_hat	100	0	1.002	0.051	0.881	1.003	1.119
theta_hat	100	0	0.076	0.187	−0.354	0.068	0.628
theta_hat_t_stats	100	0	0.412	1.084	−2.290	0.453	3.714
R2_demand	100	0	0.313	0.051	0.186	0.323	0.403
R2_supply	100	0	0.313	0.058	0.146	0.313	0.448

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.998	0.150	9.650	10.002	10.424
alpha1_hat	100	0	0.987	0.123	0.569	0.993	1.312
alpha2_hat	100	0	0.101	0.012	0.072	0.101	0.125
alpha3_hat	100	0	1.001	0.036	0.910	1.001	1.110
gamma0_hat	100	0	0.970	0.226	0.345	0.960	1.502
gamma1_hat	100	0	0.992	0.252	0.176	1.006	1.554
gamma2_hat	100	0	1.004	0.034	0.920	1.001	1.104
gamma3_hat	100	0	1.004	0.032	0.922	1.008	1.082
theta_hat	100	0	0.110	0.131	−0.196	0.093	0.498
theta_hat_t_stats	100	0	0.872	1.015	−1.513	0.796	3.817
R2_demand	100	0	0.312	0.040	0.198	0.314	0.415
R2_supply	100	0	0.311	0.037	0.234	0.316	0.405

\(\alpha_2 = 0.5\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.978	1.100	7.673	9.744	14.551
alpha1_hat	100	0	1.068	2.043	−3.604	1.104	9.409
alpha2_hat	100	0	0.491	0.222	−0.065	0.470	1.043
alpha3_hat	100	0	0.979	0.220	0.433	0.949	1.703
gamma0_hat	100	0	0.801	1.611	−3.806	1.089	4.233
gamma1_hat	100	0	38.189	374.984	−31.951	1.125	3750.284
gamma2_hat	100	0	1.021	0.222	0.652	0.990	1.638
gamma3_hat	100	0	1.023	0.223	0.481	0.998	1.602
theta_hat	100	0	−8.140	83.354	−833.306	0.038	6.903
theta_hat_t_stats	100	0	0.146	0.938	−2.223	0.108	2.629
R2_demand	100	0	0.441	0.308	−1.486	0.501	0.798
R2_supply	100	0	0.464	0.212	−0.390	0.518	0.820

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.938	0.726	8.691	9.844	12.232
alpha1_hat	100	0	1.088	1.283	−2.326	1.066	5.789
alpha2_hat	100	0	0.484	0.140	0.028	0.491	0.981
alpha3_hat	100	0	0.991	0.157	0.605	0.962	1.598
gamma0_hat	100	0	1.110	0.972	−1.632	1.195	3.511
gamma1_hat	100	0	0.516	4.430	−39.831	0.874	7.488
gamma2_hat	100	0	0.976	0.154	0.636	0.955	1.475
gamma3_hat	100	0	0.980	0.146	0.613	0.971	1.341
theta_hat	100	0	0.191	0.917	−0.942	0.095	8.588
theta_hat_t_stats	100	0	0.275	1.017	−2.654	0.406	3.067
R2_demand	100	0	0.469	0.192	−0.342	0.511	0.774
R2_supply	100	0	0.495	0.114	0.205	0.512	0.705

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.041	0.475	9.076	10.000	11.728
alpha1_hat	100	0	1.054	1.037	−1.468	0.926	3.057
alpha2_hat	100	0	0.500	0.112	0.204	0.497	0.780
alpha3_hat	100	0	1.010	0.110	0.765	1.016	1.246
gamma0_hat	100	0	0.874	0.770	−1.888	0.993	2.677
gamma1_hat	100	0	1.112	1.128	−1.090	1.063	4.240
gamma2_hat	100	0	1.019	0.116	0.767	1.014	1.350
gamma3_hat	100	0	0.993	0.102	0.770	0.980	1.389
theta_hat	100	0	0.094	0.214	−0.393	0.088	0.615
theta_hat_t_stats	100	0	0.403	1.029	−2.875	0.385	2.805
R2_demand	100	0	0.477	0.126	−0.315	0.500	0.643
R2_supply	100	0	0.479	0.112	0.073	0.481	0.687

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.042	0.185	9.652	10.034	10.520
alpha1_hat	100	0	0.969	0.399	−0.250	0.997	2.022
alpha2_hat	100	0	0.509	0.044	0.410	0.505	0.621
alpha3_hat	100	0	1.014	0.047	0.912	1.011	1.141
gamma0_hat	100	0	1.023	0.258	0.411	1.023	1.605
gamma1_hat	100	0	0.937	0.426	−0.057	0.947	1.992
gamma2_hat	100	0	0.996	0.041	0.920	0.992	1.102
gamma3_hat	100	0	1.002	0.040	0.920	1.002	1.118
theta_hat	100	0	0.108	0.074	−0.061	0.110	0.270
theta_hat_t_stats	100	0	1.252	0.847	−0.708	1.309	3.174
R2_demand	100	0	0.480	0.045	0.378	0.482	0.572
R2_supply	100	0	0.498	0.031	0.420	0.495	0.555

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.972	0.131	9.681	9.966	10.273
alpha1_hat	100	0	0.966	0.276	−0.048	0.946	1.588
alpha2_hat	100	0	0.500	0.029	0.443	0.499	0.601
alpha3_hat	100	0	0.997	0.031	0.923	0.993	1.096
gamma0_hat	100	0	1.012	0.207	0.396	1.033	1.514
gamma1_hat	100	0	0.965	0.351	0.208	0.947	1.764
gamma2_hat	100	0	0.999	0.028	0.933	0.997	1.081
gamma3_hat	100	0	1.000	0.030	0.938	0.997	1.084
theta_hat	100	0	0.105	0.062	−0.028	0.097	0.262
theta_hat_t_stats	100	0	1.705	0.994	−0.422	1.604	3.981
R2_demand	100	0	0.494	0.031	0.424	0.492	0.594
R2_supply	100	0	0.493	0.029	0.408	0.495	0.571

\(\alpha_2 = 1.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.038	0.939	8.563	9.859	13.464
alpha1_hat	100	0	1.139	3.316	−7.905	0.999	9.244
alpha2_hat	100	0	0.998	0.364	0.259	0.969	1.958
alpha3_hat	100	0	1.000	0.203	0.591	0.988	1.603
gamma0_hat	100	0	0.376	2.091	−14.550	0.795	3.760
gamma1_hat	100	0	1.860	5.439	−14.769	2.191	24.736
gamma2_hat	100	0	1.071	0.292	0.610	1.017	2.916
gamma3_hat	100	0	1.070	0.310	0.377	1.040	3.055
theta_hat	100	0	0.137	0.584	−1.691	0.056	2.587
theta_hat_t_stats	100	0	0.085	0.963	−3.160	0.183	2.192
R2_demand	100	0	0.501	0.210	−0.175	0.550	0.766
R2_supply	100	0	0.444	0.464	−3.432	0.529	0.766

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.998	0.699	8.589	10.008	12.681
alpha1_hat	100	0	0.966	2.437	−7.025	0.897	6.588
alpha2_hat	100	0	1.004	0.283	0.358	1.009	1.796
alpha3_hat	100	0	0.992	0.162	0.666	0.982	1.479
gamma0_hat	100	0	0.748	0.990	−1.939	0.766	3.205
gamma1_hat	100	0	0.915	3.725	−13.519	1.156	11.311
gamma2_hat	100	0	1.033	0.153	0.603	1.022	1.462
gamma3_hat	100	0	1.025	0.130	0.778	1.029	1.371
theta_hat	100	0	0.145	0.384	−0.731	0.104	1.793
theta_hat_t_stats	100	0	0.380	1.064	−2.135	0.468	2.402
R2_demand	100	0	0.535	0.142	0.009	0.559	0.772
R2_supply	100	0	0.520	0.122	0.117	0.537	0.764

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.052	0.470	9.294	9.975	11.816
alpha1_hat	100	0	0.985	1.597	−3.600	1.158	5.063
alpha2_hat	100	0	1.013	0.187	0.547	0.993	1.675
alpha3_hat	100	0	1.009	0.109	0.786	1.004	1.354
gamma0_hat	100	0	0.961	0.587	−1.124	0.952	2.288
gamma1_hat	100	0	0.993	1.830	−3.805	0.966	5.987
gamma2_hat	100	0	1.006	0.091	0.814	0.997	1.297
gamma3_hat	100	0	1.002	0.093	0.788	1.008	1.356
theta_hat	100	0	0.102	0.176	−0.346	0.109	0.671
theta_hat_t_stats	100	0	0.548	0.931	−1.758	0.557	2.690
R2_demand	100	0	0.529	0.112	−0.065	0.552	0.714
R2_supply	100	0	0.530	0.090	0.140	0.546	0.671

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.016	0.198	9.512	9.995	10.631
alpha1_hat	100	0	1.035	0.685	−1.053	1.009	3.025
alpha2_hat	100	0	0.999	0.082	0.797	1.003	1.248
alpha3_hat	100	0	0.997	0.049	0.896	0.992	1.156
gamma0_hat	100	0	0.962	0.344	0.164	0.957	1.892
gamma1_hat	100	0	1.096	0.806	−0.830	1.103	2.837
gamma2_hat	100	0	1.004	0.050	0.886	1.007	1.116
gamma3_hat	100	0	0.997	0.048	0.864	0.997	1.141
theta_hat	100	0	0.097	0.084	−0.096	0.100	0.272
theta_hat_t_stats	100	0	1.216	1.050	−1.298	1.289	3.237
R2_demand	100	0	0.529	0.041	0.420	0.531	0.624
R2_supply	100	0	0.528	0.037	0.463	0.526	0.634

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.994	0.127	9.689	9.981	10.334
alpha1_hat	100	0	1.076	0.462	0.143	1.053	2.293
alpha2_hat	100	0	0.991	0.046	0.883	0.987	1.095
alpha3_hat	100	0	1.002	0.031	0.902	1.001	1.075
gamma0_hat	100	0	1.013	0.208	0.495	1.007	1.482
gamma1_hat	100	0	0.957	0.511	−0.863	0.995	2.257
gamma2_hat	100	0	1.000	0.029	0.922	1.001	1.081
gamma3_hat	100	0	0.996	0.033	0.923	0.996	1.069
theta_hat	100	0	0.101	0.052	−0.046	0.094	0.284
theta_hat_t_stats	100	0	1.840	0.920	−0.871	1.732	4.718
R2_demand	100	0	0.540	0.023	0.480	0.543	0.612
R2_supply	100	0	0.539	0.026	0.469	0.538	0.600

\(\alpha_2 = 5.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.972	0.721	8.034	9.826	12.227
alpha1_hat	100	0	0.732	12.626	−30.189	1.279	31.383
alpha2_hat	100	0	5.012	1.345	2.416	4.866	8.509
alpha3_hat	100	0	1.007	0.213	0.575	0.995	1.646
gamma0_hat	100	0	0.651	2.007	−7.080	1.176	3.719
gamma1_hat	100	0	0.163	15.866	−44.945	0.729	35.737
gamma2_hat	100	0	1.039	0.290	0.616	0.990	2.241
gamma3_hat	100	0	1.038	0.251	0.606	1.001	1.983
theta_hat	100	0	0.150	0.404	−0.480	0.078	1.966
theta_hat_t_stats	100	0	0.231	0.916	−1.868	0.318	1.936
R2_demand	100	0	0.563	0.203	−0.275	0.602	0.819
R2_supply	100	0	0.558	0.249	−0.887	0.633	0.817

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.938	0.567	8.736	9.990	11.303
alpha1_hat	100	0	1.609	10.753	−29.624	1.950	38.203
alpha2_hat	100	0	4.877	1.207	1.285	4.847	9.029
alpha3_hat	100	0	1.003	0.133	0.770	0.995	1.363
gamma0_hat	100	0	0.889	0.935	−2.240	0.995	3.073
gamma1_hat	100	0	−0.993	11.173	−57.032	−0.681	25.385
gamma2_hat	100	0	1.017	0.137	0.690	0.991	1.433
gamma3_hat	100	0	1.031	0.155	0.659	1.015	1.486
theta_hat	100	0	0.154	0.248	−0.318	0.129	1.411
theta_hat_t_stats	100	0	0.523	0.771	−1.730	0.541	2.136
R2_demand	100	0	0.591	0.112	0.243	0.613	0.799
R2_supply	100	0	0.587	0.115	0.136	0.611	0.769

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.030	0.447	8.912	9.959	11.050
alpha1_hat	100	0	0.800	6.976	−16.810	0.746	18.238
alpha2_hat	100	0	5.048	0.844	3.433	5.046	7.572
alpha3_hat	100	0	1.011	0.106	0.760	1.009	1.282
gamma0_hat	100	0	0.899	0.652	−0.767	0.956	2.249
gamma1_hat	100	0	1.289	7.650	−19.914	1.022	22.499
gamma2_hat	100	0	1.015	0.102	0.838	0.999	1.327
gamma3_hat	100	0	1.016	0.101	0.780	1.010	1.279
theta_hat	100	0	0.107	0.165	−0.308	0.107	0.583
theta_hat_t_stats	100	0	0.615	0.968	−2.240	0.691	2.904
R2_demand	100	0	0.576	0.088	0.266	0.592	0.736
R2_supply	100	0	0.576	0.076	0.285	0.590	0.734

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.000	0.183	9.653	9.977	10.385
alpha1_hat	100	0	1.291	2.956	−5.136	1.479	7.205
alpha2_hat	100	0	4.973	0.360	4.186	4.986	5.969
alpha3_hat	100	0	1.008	0.041	0.921	1.010	1.142
gamma0_hat	100	0	0.934	0.307	0.133	0.930	1.603
gamma1_hat	100	0	1.040	2.853	−6.274	0.913	6.886
gamma2_hat	100	0	1.008	0.047	0.881	1.004	1.116
gamma3_hat	100	0	1.008	0.041	0.923	1.013	1.109
theta_hat	100	0	0.107	0.067	−0.067	0.112	0.262
theta_hat_t_stats	100	0	1.503	0.905	−1.128	1.638	3.560
R2_demand	100	0	0.588	0.034	0.509	0.589	0.674
R2_supply	100	0	0.583	0.036	0.454	0.584	0.657

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.985	0.133	9.706	9.966	10.504
alpha1_hat	100	0	0.858	2.075	−4.874	0.888	6.281
alpha2_hat	100	0	4.998	0.252	4.389	4.956	5.689
alpha3_hat	100	0	0.998	0.028	0.949	0.999	1.086
gamma0_hat	100	0	1.003	0.210	0.418	0.995	1.624
gamma1_hat	100	0	0.824	2.211	−4.046	0.848	6.384
gamma2_hat	100	0	0.999	0.030	0.925	1.001	1.076
gamma3_hat	100	0	1.003	0.038	0.910	1.004	1.096
theta_hat	100	0	0.104	0.054	−0.024	0.105	0.218
theta_hat_t_stats	100	0	2.106	1.054	−0.536	2.193	4.360
R2_demand	100	0	0.589	0.025	0.499	0.591	0.629
R2_supply	100	0	0.585	0.024	0.536	0.588	0.632

\(\alpha_2 = 20.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.009	0.849	8.005	9.985	12.852
alpha1_hat	100	0	−1.334	57.303	−166.001	−4.268	170.300
alpha2_hat	100	0	20.221	6.912	0.669	19.854	41.702
alpha3_hat	100	0	0.983	0.197	0.505	0.978	1.448
gamma0_hat	100	0	0.537	2.043	−8.719	0.972	3.459
gamma1_hat	100	0	−24.302	161.538	−1481.399	−2.022	182.283
gamma2_hat	100	0	1.057	0.237	0.517	1.042	1.888
gamma3_hat	100	0	1.070	0.303	0.590	1.021	2.912
theta_hat	100	0	0.311	0.970	−0.520	0.131	8.392
theta_hat_t_stats	100	0	0.371	0.953	−2.341	0.449	2.521
R2_demand	100	0	0.585	0.161	−0.060	0.619	0.858
R2_supply	100	0	0.551	0.385	−1.836	0.642	0.812

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.136	0.644	8.713	10.140	11.647
alpha1_hat	100	0	−0.463	41.128	−102.521	0.213	130.323
alpha2_hat	100	0	20.640	4.822	8.791	20.220	31.189
alpha3_hat	100	0	1.009	0.145	0.699	1.004	1.313
gamma0_hat	100	0	0.813	1.015	−2.678	0.853	2.763
gamma1_hat	100	0	4.002	41.292	−96.370	7.400	91.148
gamma2_hat	100	0	1.025	0.163	0.713	1.016	1.521
gamma3_hat	100	0	1.011	0.142	0.715	1.001	1.375
theta_hat	100	0	0.098	0.220	−0.341	0.084	0.571
theta_hat_t_stats	100	0	0.381	0.963	−1.942	0.392	2.439
R2_demand	100	0	0.563	0.146	0.035	0.586	0.793
R2_supply	100	0	0.593	0.111	0.091	0.594	0.809

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.963	0.437	9.013	9.902	11.204
alpha1_hat	100	0	−3.256	26.239	−73.104	−0.447	61.611
alpha2_hat	100	0	20.285	3.231	13.759	20.306	30.019
alpha3_hat	100	0	0.998	0.111	0.765	0.996	1.329
gamma0_hat	100	0	0.929	0.673	−0.988	0.894	2.180
gamma1_hat	100	0	0.661	24.494	−77.505	−0.298	98.402
gamma2_hat	100	0	1.009	0.098	0.736	1.014	1.221
gamma3_hat	100	0	1.016	0.103	0.789	1.010	1.261
theta_hat	100	0	0.113	0.146	−0.378	0.121	0.502
theta_hat_t_stats	100	0	0.671	0.910	−2.384	0.731	2.716
R2_demand	100	0	0.594	0.078	0.364	0.594	0.772
R2_supply	100	0	0.596	0.061	0.433	0.594	0.727

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.995	0.207	9.460	10.015	10.476
alpha1_hat	100	0	0.251	10.457	−23.319	2.316	21.523
alpha2_hat	100	0	20.076	1.288	16.737	19.948	23.231
alpha3_hat	100	0	0.999	0.049	0.851	0.997	1.119
gamma0_hat	100	0	0.926	0.347	0.042	0.883	1.556
gamma1_hat	100	0	1.692	10.652	−19.769	1.393	33.092
gamma2_hat	100	0	1.011	0.049	0.918	1.004	1.140
gamma3_hat	100	0	1.013	0.043	0.903	1.013	1.136
theta_hat	100	0	0.104	0.063	−0.039	0.113	0.223
theta_hat_t_stats	100	0	1.505	0.888	−0.547	1.621	3.152
R2_demand	100	0	0.595	0.039	0.461	0.595	0.667
R2_supply	100	0	0.593	0.033	0.510	0.594	0.667

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.992	0.142	9.640	9.988	10.326
alpha1_hat	100	0	0.453	8.219	−19.675	0.204	15.929
alpha2_hat	100	0	20.017	0.956	17.485	20.057	22.606
alpha3_hat	100	0	0.995	0.034	0.903	0.992	1.085
gamma0_hat	100	0	1.018	0.211	0.483	1.011	1.452
gamma1_hat	100	0	1.081	8.878	−18.857	−0.398	24.715
gamma2_hat	100	0	0.993	0.029	0.923	0.995	1.076
gamma3_hat	100	0	1.002	0.031	0.938	1.002	1.084
theta_hat	100	0	0.101	0.051	−0.045	0.098	0.224
theta_hat_t_stats	100	0	2.088	0.999	−0.978	2.101	4.154
R2_demand	100	0	0.597	0.026	0.518	0.600	0.642
R2_supply	100	0	0.593	0.026	0.533	0.592	0.655

\(\theta = 0.2\)

\(\alpha_2 = 0.1\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.075	1.011	7.398	10.061	13.437
alpha1_hat	100	0	1.091	0.872	−0.569	1.004	5.993
alpha2_hat	100	0	0.095	0.088	−0.270	0.097	0.283
alpha3_hat	100	0	1.004	0.238	0.588	0.981	1.694
gamma0_hat	100	0	0.548	1.504	−4.717	0.941	3.049
gamma1_hat	100	0	2.574	22.776	−74.725	0.963	166.484
gamma2_hat	100	0	1.045	0.217	0.601	1.008	1.542
gamma3_hat	100	0	1.037	0.220	0.567	0.996	1.582
theta_hat	100	0	−0.708	13.455	−106.414	0.266	40.890
theta_hat_t_stats	100	0	0.272	1.032	−2.096	0.262	2.472
R2_demand	100	0	0.229	0.389	−1.627	0.339	0.609
R2_supply	100	0	0.206	0.285	−0.901	0.305	0.694

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.926	0.661	8.653	9.862	11.727
alpha1_hat	100	0	0.794	0.635	−0.550	0.785	2.855
alpha2_hat	100	0	0.117	0.064	−0.036	0.113	0.357
alpha3_hat	100	0	1.000	0.145	0.676	0.988	1.460
gamma0_hat	100	0	0.863	0.947	−1.332	1.010	2.758
gamma1_hat	100	0	0.879	2.071	−9.676	0.990	11.014
gamma2_hat	100	0	1.017	0.143	0.765	1.001	1.382
gamma3_hat	100	0	1.030	0.141	0.629	1.032	1.427
theta_hat	100	0	0.277	1.101	−5.315	0.223	5.698
theta_hat_t_stats	100	0	0.385	0.951	−1.791	0.365	2.645
R2_demand	100	0	0.269	0.185	−0.489	0.302	0.527
R2_supply	100	0	0.265	0.180	−0.455	0.281	0.573

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.959	0.434	8.882	9.918	11.708
alpha1_hat	100	0	0.941	0.458	−0.074	0.949	2.347
alpha2_hat	100	0	0.104	0.043	−0.022	0.102	0.237
alpha3_hat	100	0	1.001	0.102	0.755	0.998	1.358
gamma0_hat	100	0	0.948	0.712	−1.078	0.975	2.415
gamma1_hat	100	0	0.951	1.194	−2.037	1.051	7.303
gamma2_hat	100	0	1.005	0.112	0.712	1.001	1.284
gamma3_hat	100	0	1.007	0.102	0.747	1.012	1.239
theta_hat	100	0	0.256	0.636	−2.813	0.175	2.333
theta_hat_t_stats	100	0	0.486	1.017	−2.527	0.456	2.639
R2_demand	100	0	0.264	0.137	−0.149	0.274	0.532
R2_supply	100	0	0.260	0.124	−0.197	0.272	0.466

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.031	0.176	9.642	10.023	10.461
alpha1_hat	100	0	1.010	0.190	0.643	1.021	1.701
alpha2_hat	100	0	0.101	0.019	0.043	0.098	0.152
alpha3_hat	100	0	1.008	0.037	0.932	1.008	1.111
gamma0_hat	100	0	1.029	0.337	0.179	1.029	2.079
gamma1_hat	100	0	1.003	0.370	−0.138	1.008	1.761
gamma2_hat	100	0	0.993	0.051	0.846	0.990	1.116
gamma3_hat	100	0	0.995	0.046	0.880	0.995	1.112
theta_hat	100	0	0.196	0.191	−0.243	0.175	0.747
theta_hat_t_stats	100	0	0.998	0.913	−1.285	1.012	3.137
R2_demand	100	0	0.264	0.056	0.134	0.271	0.373
R2_supply	100	0	0.272	0.050	0.111	0.273	0.364

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.008	0.132	9.671	10.024	10.394
alpha1_hat	100	0	1.011	0.132	0.646	1.015	1.329
alpha2_hat	100	0	0.099	0.012	0.069	0.098	0.137
alpha3_hat	100	0	0.999	0.030	0.918	1.001	1.077
gamma0_hat	100	0	0.952	0.212	0.394	0.966	1.475
gamma1_hat	100	0	0.962	0.256	0.461	0.970	1.765
gamma2_hat	100	0	1.005	0.030	0.929	1.004	1.069
gamma3_hat	100	0	1.005	0.031	0.925	1.003	1.075
theta_hat	100	0	0.229	0.137	−0.166	0.216	0.521
theta_hat_t_stats	100	0	1.695	0.961	−1.275	1.658	3.443
R2_demand	100	0	0.276	0.042	0.161	0.276	0.375
R2_supply	100	0	0.269	0.037	0.170	0.273	0.362

\(\alpha_2 = 0.5\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.931	0.852	7.610	9.913	12.363
alpha1_hat	100	0	0.945	2.071	−5.565	0.842	6.752
alpha2_hat	100	0	0.494	0.218	−0.055	0.491	1.175
alpha3_hat	100	0	0.991	0.212	0.508	0.965	1.470
gamma0_hat	100	0	0.902	1.615	−6.741	1.067	4.386
gamma1_hat	100	0	0.035	4.734	−35.358	0.795	6.217
gamma2_hat	100	0	0.995	0.212	0.588	0.980	1.714
gamma3_hat	100	0	0.989	0.210	0.510	0.993	1.529
theta_hat	100	0	0.415	0.873	−0.539	0.234	5.647
theta_hat_t_stats	100	0	0.499	0.890	−1.713	0.593	2.092
R2_demand	100	0	0.366	0.272	−0.637	0.422	0.733
R2_supply	100	0	0.443	0.229	−0.644	0.481	0.799

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.000	0.609	8.668	9.966	11.644
alpha1_hat	100	0	0.873	1.411	−2.676	0.841	4.144
alpha2_hat	100	0	0.514	0.145	0.207	0.512	1.042
alpha3_hat	100	0	1.013	0.139	0.662	1.010	1.360
gamma0_hat	100	0	0.886	1.115	−2.705	1.022	2.746
gamma1_hat	100	0	0.820	1.754	−4.287	0.737	5.277
gamma2_hat	100	0	1.015	0.163	0.761	0.999	1.562
gamma3_hat	100	0	1.008	0.169	0.710	0.971	1.518
theta_hat	100	0	0.249	0.361	−0.511	0.216	1.569
theta_hat_t_stats	100	0	0.703	0.940	−1.470	0.733	3.272
R2_demand	100	0	0.411	0.176	−0.371	0.446	0.713
R2_supply	100	0	0.424	0.154	−0.248	0.446	0.663

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.971	0.392	9.083	9.932	11.142
alpha1_hat	100	0	0.983	1.008	−1.916	1.021	3.446
alpha2_hat	100	0	0.498	0.106	0.255	0.489	0.800
alpha3_hat	100	0	0.983	0.095	0.814	0.981	1.286
gamma0_hat	100	0	0.755	0.696	−1.330	0.714	2.564
gamma1_hat	100	0	0.811	1.349	−2.427	0.846	4.138
gamma2_hat	100	0	1.028	0.098	0.814	1.018	1.310
gamma3_hat	100	0	1.031	0.095	0.803	1.030	1.332
theta_hat	100	0	0.273	0.238	−0.289	0.268	0.956
theta_hat_t_stats	100	0	1.127	0.927	−1.723	1.083	3.000
R2_demand	100	0	0.426	0.108	0.137	0.451	0.643
R2_supply	100	0	0.407	0.117	−0.046	0.403	0.639

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.028	0.204	9.613	10.024	10.608
alpha1_hat	100	0	1.011	0.439	0.159	1.018	2.029
alpha2_hat	100	0	0.503	0.053	0.384	0.510	0.622
alpha3_hat	100	0	1.010	0.046	0.915	1.012	1.112
gamma0_hat	100	0	0.976	0.312	0.207	0.961	2.034
gamma1_hat	100	0	0.925	0.569	−0.508	0.882	2.970
gamma2_hat	100	0	1.002	0.047	0.860	1.003	1.134
gamma3_hat	100	0	1.003	0.042	0.882	1.001	1.118
theta_hat	100	0	0.215	0.110	−0.181	0.202	0.513
theta_hat_t_stats	100	0	2.230	1.047	−1.911	2.222	5.614
R2_demand	100	0	0.425	0.045	0.296	0.425	0.511
R2_supply	100	0	0.425	0.048	0.279	0.424	0.537

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.001	0.135	9.705	9.999	10.503
alpha1_hat	100	0	1.015	0.304	0.296	1.053	1.931
alpha2_hat	100	0	0.499	0.031	0.434	0.495	0.592
alpha3_hat	100	0	1.002	0.030	0.923	1.002	1.124
gamma0_hat	100	0	0.988	0.211	0.491	1.000	1.475
gamma1_hat	100	0	0.940	0.370	0.050	0.914	1.805
gamma2_hat	100	0	1.000	0.030	0.932	0.998	1.068
gamma3_hat	100	0	1.001	0.030	0.912	1.002	1.077
theta_hat	100	0	0.213	0.065	0.038	0.224	0.324
theta_hat_t_stats	100	0	3.165	0.942	0.601	3.287	4.820
R2_demand	100	0	0.429	0.035	0.313	0.426	0.516
R2_supply	100	0	0.426	0.029	0.351	0.428	0.486

\(\alpha_2 = 1.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.040	1.033	8.325	9.983	14.154
alpha1_hat	100	0	0.732	3.527	−7.984	0.989	13.497
alpha2_hat	100	0	1.034	0.395	−0.040	0.982	2.165
alpha3_hat	100	0	1.018	0.228	0.547	1.015	2.066
gamma0_hat	100	0	0.685	1.396	−3.283	0.908	3.717
gamma1_hat	100	0	−0.548	14.792	−137.315	1.171	18.350
gamma2_hat	100	0	1.035	0.209	0.596	1.011	1.701
gamma3_hat	100	0	1.052	0.237	0.534	1.020	1.689
theta_hat	100	0	0.374	1.192	−1.655	0.165	10.772
theta_hat_t_stats	100	0	0.539	1.091	−2.646	0.446	3.378
R2_demand	100	0	0.442	0.271	−1.045	0.510	0.773
R2_supply	100	0	0.463	0.209	−0.202	0.503	0.849

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.888	0.665	8.647	9.810	11.863
alpha1_hat	100	0	1.235	2.322	−4.598	1.410	5.977
alpha2_hat	100	0	0.950	0.277	0.235	0.969	1.804
alpha3_hat	100	0	0.979	0.162	0.634	0.967	1.363
gamma0_hat	100	0	0.991	0.985	−1.499	1.034	3.186
gamma1_hat	100	0	0.778	3.913	−17.340	1.335	8.883
gamma2_hat	100	0	0.993	0.143	0.652	0.984	1.396
gamma3_hat	100	0	1.015	0.159	0.660	0.995	1.431
theta_hat	100	0	0.246	0.429	−0.645	0.184	2.547
theta_hat_t_stats	100	0	0.639	1.071	−1.637	0.676	3.217
R2_demand	100	0	0.474	0.143	−0.081	0.508	0.740
R2_supply	100	0	0.472	0.128	0.150	0.507	0.695

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.989	0.402	9.067	9.978	10.821
alpha1_hat	100	0	0.892	1.662	−2.511	0.818	5.197
alpha2_hat	100	0	1.010	0.174	0.651	1.021	1.376
alpha3_hat	100	0	1.008	0.093	0.737	1.010	1.240
gamma0_hat	100	0	0.895	0.701	−1.357	0.977	2.249
gamma1_hat	100	0	1.147	1.722	−3.622	1.101	5.098
gamma2_hat	100	0	1.018	0.107	0.777	1.008	1.352
gamma3_hat	100	0	1.013	0.098	0.841	1.005	1.347
theta_hat	100	0	0.198	0.183	−0.195	0.210	0.722
theta_hat_t_stats	100	0	0.970	0.895	−0.912	1.048	2.782
R2_demand	100	0	0.475	0.105	0.002	0.487	0.678
R2_supply	100	0	0.467	0.099	0.056	0.481	0.651

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.988	0.171	9.578	9.975	10.431
alpha1_hat	100	0	0.821	0.715	−0.816	0.789	2.254
alpha2_hat	100	0	1.015	0.078	0.850	1.014	1.272
alpha3_hat	100	0	0.997	0.042	0.893	1.000	1.083
gamma0_hat	100	0	0.963	0.309	0.199	0.954	1.754
gamma1_hat	100	0	1.064	0.759	−0.706	1.039	3.020
gamma2_hat	100	0	1.004	0.045	0.875	1.004	1.105
gamma3_hat	100	0	1.003	0.044	0.893	1.005	1.115
theta_hat	100	0	0.201	0.078	0.025	0.204	0.366
theta_hat_t_stats	100	0	2.413	0.878	0.311	2.459	4.222
R2_demand	100	0	0.473	0.043	0.342	0.479	0.554
R2_supply	100	0	0.470	0.043	0.356	0.470	0.578

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.996	0.145	9.645	9.980	10.376
alpha1_hat	100	0	1.038	0.491	0.048	1.017	2.282
alpha2_hat	100	0	0.995	0.058	0.795	0.986	1.122
alpha3_hat	100	0	1.000	0.032	0.908	1.001	1.091
gamma0_hat	100	0	0.962	0.217	0.315	0.979	1.463
gamma1_hat	100	0	1.026	0.641	−0.504	1.069	2.565
gamma2_hat	100	0	1.004	0.034	0.933	1.000	1.087
gamma3_hat	100	0	1.001	0.031	0.910	1.003	1.110
theta_hat	100	0	0.204	0.064	0.042	0.199	0.377
theta_hat_t_stats	100	0	3.397	0.972	0.804	3.354	5.773
R2_demand	100	0	0.479	0.035	0.380	0.483	0.534
R2_supply	100	0	0.472	0.028	0.404	0.472	0.545

\(\alpha_2 = 5.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.002	1.058	7.983	9.898	14.800
alpha1_hat	100	0	1.377	15.017	−48.230	0.894	38.341
alpha2_hat	100	0	4.940	1.918	0.544	4.849	15.191
alpha3_hat	100	0	1.006	0.242	0.572	0.991	2.311
gamma0_hat	100	0	0.511	1.736	−5.222	0.866	3.351
gamma1_hat	100	0	−4.801	27.217	−157.492	1.365	32.063
gamma2_hat	100	0	1.067	0.272	0.558	1.023	2.006
gamma3_hat	100	0	1.058	0.206	0.657	1.021	1.673
theta_hat	100	0	0.391	0.651	−0.854	0.264	3.853
theta_hat_t_stats	100	0	0.655	0.933	−3.120	0.694	2.744
R2_demand	100	0	0.506	0.292	−1.126	0.570	0.816
R2_supply	100	0	0.493	0.231	−0.546	0.550	0.794

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.019	0.671	8.679	10.062	12.231
alpha1_hat	100	0	2.664	10.353	−18.538	1.161	33.037
alpha2_hat	100	0	4.837	1.178	1.936	4.857	7.383
alpha3_hat	100	0	1.002	0.139	0.698	0.996	1.357
gamma0_hat	100	0	0.999	0.967	−1.678	1.054	3.016
gamma1_hat	100	0	−0.080	11.572	−49.144	0.659	23.910
gamma2_hat	100	0	0.993	0.160	0.569	0.981	1.481
gamma3_hat	100	0	0.997	0.155	0.681	0.995	1.343
theta_hat	100	0	0.235	0.280	−0.298	0.192	1.542
theta_hat_t_stats	100	0	0.775	0.816	−1.355	0.739	2.769
R2_demand	100	0	0.507	0.151	−0.049	0.532	0.741
R2_supply	100	0	0.530	0.121	0.133	0.545	0.762

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.955	0.387	9.235	9.913	11.116
alpha1_hat	100	0	0.953	6.612	−20.606	1.011	18.557
alpha2_hat	100	0	4.949	0.771	3.250	4.930	7.343
alpha3_hat	100	0	0.980	0.087	0.739	0.973	1.348
gamma0_hat	100	0	0.897	0.786	−1.441	1.018	2.274
gamma1_hat	100	0	0.073	7.274	−23.077	0.463	18.307
gamma2_hat	100	0	1.013	0.114	0.813	0.995	1.324
gamma3_hat	100	0	1.007	0.110	0.743	1.009	1.265
theta_hat	100	0	0.238	0.176	−0.171	0.218	0.814
theta_hat_t_stats	100	0	1.266	0.860	−1.171	1.262	2.948
R2_demand	100	0	0.521	0.102	0.148	0.532	0.682
R2_supply	100	0	0.505	0.101	0.201	0.524	0.676

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.982	0.193	9.560	9.971	10.435
alpha1_hat	100	0	1.092	3.330	−6.629	0.974	7.706
alpha2_hat	100	0	4.972	0.378	4.148	5.007	5.920
alpha3_hat	100	0	0.992	0.049	0.891	0.986	1.130
gamma0_hat	100	0	0.945	0.330	−0.030	0.942	1.641
gamma1_hat	100	0	0.908	3.676	−7.279	0.801	10.889
gamma2_hat	100	0	1.006	0.047	0.896	1.008	1.126
gamma3_hat	100	0	1.013	0.047	0.900	1.010	1.109
theta_hat	100	0	0.211	0.078	0.001	0.211	0.369
theta_hat_t_stats	100	0	2.746	0.945	0.017	2.874	4.744
R2_demand	100	0	0.521	0.039	0.432	0.517	0.609
R2_supply	100	0	0.517	0.039	0.408	0.522	0.604

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.999	0.134	9.692	10.002	10.278
alpha1_hat	100	0	1.050	2.303	−6.558	1.026	6.791
alpha2_hat	100	0	4.995	0.248	4.188	4.964	5.820
alpha3_hat	100	0	1.002	0.030	0.929	1.001	1.072
gamma0_hat	100	0	0.983	0.216	0.423	0.979	1.454
gamma1_hat	100	0	0.878	2.265	−4.816	0.770	6.018
gamma2_hat	100	0	1.003	0.033	0.915	1.000	1.104
gamma3_hat	100	0	0.995	0.031	0.916	1.001	1.074
theta_hat	100	0	0.205	0.052	0.093	0.209	0.337
theta_hat_t_stats	100	0	3.838	0.892	1.855	3.918	6.058
R2_demand	100	0	0.519	0.029	0.437	0.521	0.587
R2_supply	100	0	0.517	0.027	0.437	0.514	0.566

\(\alpha_2 = 20.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.907	0.938	7.866	9.809	12.850
alpha1_hat	100	0	1.370	51.562	−120.993	−5.489	170.972
alpha2_hat	100	0	19.581	6.126	3.832	19.461	40.350
alpha3_hat	100	0	0.994	0.232	0.524	0.955	1.846
gamma0_hat	100	0	0.408	2.155	−9.663	0.710	4.317
gamma1_hat	100	0	6.310	89.940	−415.311	10.375	192.299
gamma2_hat	100	0	1.058	0.282	0.548	1.047	2.227
gamma3_hat	100	0	1.080	0.347	0.632	1.011	2.963
theta_hat	100	0	0.262	0.494	−0.626	0.172	2.440
theta_hat_t_stats	100	0	0.423	0.913	−2.026	0.516	2.709
R2_demand	100	0	0.504	0.230	−0.385	0.553	0.813
R2_supply	100	0	0.451	0.365	−2.320	0.541	0.816

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.964	0.590	8.849	9.864	12.076
alpha1_hat	100	0	−6.842	38.993	−106.509	−8.018	94.391
alpha2_hat	100	0	20.716	4.666	11.087	20.285	34.440
alpha3_hat	100	0	0.994	0.129	0.703	0.993	1.496
gamma0_hat	100	0	1.017	1.082	−2.746	1.186	2.885
gamma1_hat	100	0	−0.088	44.747	−150.445	1.305	160.906
gamma2_hat	100	0	1.003	0.161	0.668	0.977	1.508
gamma3_hat	100	0	0.978	0.148	0.646	0.972	1.490
theta_hat	100	0	0.206	0.265	−0.593	0.154	1.063
theta_hat_t_stats	100	0	0.767	0.882	−1.602	0.700	2.806
R2_demand	100	0	0.526	0.168	−0.418	0.558	0.786
R2_supply	100	0	0.546	0.115	0.195	0.570	0.718

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.041	0.450	9.145	10.047	11.300
alpha1_hat	100	0	3.898	32.444	−76.175	2.590	80.157
alpha2_hat	100	0	19.927	3.680	12.924	19.748	32.442
alpha3_hat	100	0	1.025	0.102	0.792	1.028	1.270
gamma0_hat	100	0	1.040	0.623	−0.460	1.052	2.627
gamma1_hat	100	0	−4.063	25.418	−65.590	−4.101	47.477
gamma2_hat	100	0	0.990	0.095	0.707	0.983	1.242
gamma3_hat	100	0	1.003	0.099	0.771	0.997	1.234
theta_hat	100	0	0.222	0.151	−0.115	0.210	0.605
theta_hat_t_stats	100	0	1.242	0.758	−0.918	1.286	2.638
R2_demand	100	0	0.517	0.094	0.251	0.529	0.722
R2_supply	100	0	0.523	0.085	0.209	0.541	0.655

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.986	0.172	9.642	9.959	10.463
alpha1_hat	100	0	1.846	13.554	−32.313	1.997	35.088
alpha2_hat	100	0	19.849	1.481	16.789	19.801	23.422
alpha3_hat	100	0	0.995	0.044	0.904	0.992	1.124
gamma0_hat	100	0	1.037	0.276	0.146	1.034	1.619
gamma1_hat	100	0	−0.142	13.378	−30.588	−1.968	38.986
gamma2_hat	100	0	0.997	0.040	0.914	0.993	1.104
gamma3_hat	100	0	0.998	0.046	0.907	0.993	1.134
theta_hat	100	0	0.202	0.076	0.026	0.211	0.375
theta_hat_t_stats	100	0	2.699	0.965	0.373	2.843	5.085
R2_demand	100	0	0.531	0.041	0.385	0.536	0.609
R2_supply	100	0	0.534	0.033	0.431	0.534	0.645

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.989	0.154	9.663	9.990	10.370
alpha1_hat	100	0	2.484	8.549	−26.399	3.687	21.425
alpha2_hat	100	0	19.802	1.119	17.548	19.748	23.647
alpha3_hat	100	0	0.999	0.034	0.918	1.000	1.075
gamma0_hat	100	0	0.989	0.192	0.541	0.985	1.465
gamma1_hat	100	0	1.404	9.574	−24.190	1.093	20.914
gamma2_hat	100	0	1.003	0.029	0.919	1.002	1.087
gamma3_hat	100	0	0.998	0.031	0.928	1.000	1.061
theta_hat	100	0	0.199	0.053	0.077	0.196	0.329
theta_hat_t_stats	100	0	3.772	0.896	1.580	3.739	5.662
R2_demand	100	0	0.530	0.029	0.470	0.531	0.594
R2_supply	100	0	0.527	0.024	0.466	0.527	0.599

\(\theta = 0.33\)

\(\alpha_2 = 0.1\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.101	0.903	7.916	10.022	12.702
alpha1_hat	100	0	1.053	1.063	−1.100	0.896	4.684
alpha2_hat	100	0	0.102	0.093	−0.171	0.098	0.323
alpha3_hat	100	0	1.003	0.219	0.569	0.991	1.623
gamma0_hat	100	0	1.065	1.516	−4.142	1.438	4.185
gamma1_hat	100	0	4.401	33.922	−15.564	1.224	337.594
gamma2_hat	100	0	0.982	0.211	0.382	0.949	1.643
gamma3_hat	100	0	0.981	0.200	0.535	0.958	1.596
theta_hat	100	0	−1.026	13.210	−129.878	0.127	9.248
theta_hat_t_stats	100	0	0.150	0.935	−2.170	0.180	2.524
R2_demand	100	0	0.169	0.305	−0.935	0.247	0.609
R2_supply	100	0	0.233	0.276	−0.713	0.264	0.733

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.942	0.645	8.511	9.888	11.803
alpha1_hat	100	0	1.035	0.659	−1.098	1.009	2.949
alpha2_hat	100	0	0.094	0.060	−0.039	0.092	0.305
alpha3_hat	100	0	1.003	0.158	0.666	0.989	1.558
gamma0_hat	100	0	1.035	1.136	−2.674	1.152	2.769
gamma1_hat	100	0	1.637	6.820	−14.264	0.813	52.629
gamma2_hat	100	0	0.995	0.166	0.703	0.966	1.457
gamma3_hat	100	0	0.999	0.160	0.665	0.985	1.541
theta_hat	100	0	−0.004	3.435	−26.394	0.403	8.146
theta_hat_t_stats	100	0	0.438	0.969	−1.833	0.528	2.155
R2_demand	100	0	0.245	0.153	−0.357	0.283	0.542
R2_supply	100	0	0.242	0.197	−0.353	0.277	0.604

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.021	0.418	9.172	9.970	11.266
alpha1_hat	100	0	1.039	0.462	−0.247	0.990	2.050
alpha2_hat	100	0	0.097	0.042	−0.003	0.096	0.235
alpha3_hat	100	0	1.008	0.096	0.801	1.004	1.253
gamma0_hat	100	0	0.854	0.652	−0.964	0.852	2.344
gamma1_hat	100	0	0.661	1.543	−11.142	0.899	4.071
gamma2_hat	100	0	1.014	0.094	0.837	1.006	1.252
gamma3_hat	100	0	1.026	0.101	0.817	1.024	1.278
theta_hat	100	0	0.529	0.745	−0.976	0.379	6.205
theta_hat_t_stats	100	0	0.911	0.748	−0.853	0.832	2.497
R2_demand	100	0	0.230	0.134	−0.151	0.238	0.537
R2_supply	100	0	0.211	0.145	−0.245	0.219	0.473

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.987	0.203	9.377	9.972	10.663
alpha1_hat	100	0	1.005	0.200	0.332	1.003	1.444
alpha2_hat	100	0	0.099	0.020	0.053	0.101	0.155
alpha3_hat	100	0	1.004	0.048	0.843	1.004	1.118
gamma0_hat	100	0	1.011	0.300	0.171	1.027	1.736
gamma1_hat	100	0	0.959	0.411	−0.356	0.954	1.920
gamma2_hat	100	0	0.995	0.050	0.861	0.996	1.121
gamma3_hat	100	0	1.008	0.038	0.926	1.003	1.103
theta_hat	100	0	0.355	0.213	−0.201	0.351	1.184
theta_hat_t_stats	100	0	1.713	0.967	−1.073	1.808	4.122
R2_demand	100	0	0.241	0.058	0.101	0.249	0.371
R2_supply	100	0	0.237	0.061	0.116	0.239	0.366

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.010	0.136	9.632	10.018	10.284
alpha1_hat	100	0	1.010	0.130	0.719	1.001	1.343
alpha2_hat	100	0	0.099	0.014	0.067	0.098	0.142
alpha3_hat	100	0	0.998	0.033	0.931	0.999	1.087
gamma0_hat	100	0	1.007	0.192	0.438	1.037	1.375
gamma1_hat	100	0	0.948	0.311	0.071	0.921	1.874
gamma2_hat	100	0	0.998	0.031	0.924	0.998	1.103
gamma3_hat	100	0	0.998	0.027	0.943	0.998	1.076
theta_hat	100	0	0.354	0.156	−0.140	0.352	0.801
theta_hat_t_stats	100	0	2.481	1.054	−1.044	2.525	4.915
R2_demand	100	0	0.230	0.042	0.126	0.223	0.333
R2_supply	100	0	0.237	0.039	0.152	0.235	0.331

\(\alpha_2 = 0.5\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.788	0.869	7.639	9.751	13.200
alpha1_hat	100	0	0.846	2.077	−3.651	0.938	6.905
alpha2_hat	100	0	0.484	0.233	−0.058	0.490	1.293
alpha3_hat	100	0	0.971	0.219	0.492	0.951	1.737
gamma0_hat	100	0	1.061	1.365	−2.315	1.101	4.408
gamma1_hat	100	0	0.042	22.643	−146.792	1.182	118.213
gamma2_hat	100	0	1.002	0.196	0.603	0.988	1.425
gamma3_hat	100	0	0.992	0.190	0.624	0.982	1.567
theta_hat	100	0	0.513	4.245	−17.446	0.260	27.957
theta_hat_t_stats	100	0	0.510	0.974	−3.851	0.583	2.632
R2_demand	100	0	0.366	0.273	−1.213	0.436	0.762
R2_supply	100	0	0.367	0.246	−0.378	0.424	0.800

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.124	0.601	8.625	10.097	11.521
alpha1_hat	100	0	0.972	1.435	−3.407	0.881	5.203
alpha2_hat	100	0	0.523	0.162	0.116	0.529	0.973
alpha3_hat	100	0	1.044	0.148	0.716	1.051	1.519
gamma0_hat	100	0	1.200	0.851	−0.579	1.262	3.107
gamma1_hat	100	0	1.052	1.975	−4.719	1.070	7.520
gamma2_hat	100	0	0.985	0.126	0.697	0.989	1.263
gamma3_hat	100	0	0.976	0.136	0.557	0.973	1.354
theta_hat	100	0	0.282	0.345	−0.644	0.258	1.505
theta_hat_t_stats	100	0	0.783	0.806	−1.187	0.956	2.203
R2_demand	100	0	0.314	0.194	−0.334	0.351	0.618
R2_supply	100	0	0.409	0.142	−0.110	0.432	0.686

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.969	0.451	8.923	9.933	11.168
alpha1_hat	100	0	0.994	1.062	−2.433	0.846	4.063
alpha2_hat	100	0	0.496	0.109	0.221	0.488	0.786
alpha3_hat	100	0	0.999	0.116	0.726	1.009	1.273
gamma0_hat	100	0	1.154	0.607	−0.438	1.157	2.422
gamma1_hat	100	0	0.901	1.635	−3.139	0.952	4.285
gamma2_hat	100	0	0.979	0.087	0.767	0.975	1.239
gamma3_hat	100	0	0.997	0.105	0.723	0.989	1.348
theta_hat	100	0	0.329	0.285	−0.214	0.290	1.076
theta_hat_t_stats	100	0	1.306	1.048	−0.894	1.256	3.955
R2_demand	100	0	0.357	0.115	0.000	0.379	0.556
R2_supply	100	0	0.374	0.112	0.096	0.382	0.596

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.989	0.216	9.527	9.985	10.570
alpha1_hat	100	0	0.921	0.428	−0.146	0.935	2.314
alpha2_hat	100	0	0.506	0.054	0.332	0.504	0.620
alpha3_hat	100	0	1.000	0.042	0.899	1.000	1.119
gamma0_hat	100	0	1.017	0.287	−0.045	1.054	1.589
gamma1_hat	100	0	1.098	0.555	−0.208	1.035	2.450
gamma2_hat	100	0	1.000	0.042	0.899	1.005	1.117
gamma3_hat	100	0	1.000	0.043	0.897	0.994	1.095
theta_hat	100	0	0.311	0.105	0.044	0.306	0.590
theta_hat_t_stats	100	0	3.020	0.907	0.415	3.118	4.864
R2_demand	100	0	0.355	0.058	0.160	0.364	0.475
R2_supply	100	0	0.365	0.045	0.234	0.363	0.469

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.983	0.126	9.699	9.986	10.273
alpha1_hat	100	0	0.951	0.318	0.161	0.927	1.761
alpha2_hat	100	0	0.503	0.034	0.427	0.500	0.587
alpha3_hat	100	0	0.996	0.031	0.916	0.995	1.082
gamma0_hat	100	0	0.978	0.216	0.407	0.992	1.508
gamma1_hat	100	0	1.010	0.402	0.062	1.028	1.965
gamma2_hat	100	0	1.006	0.030	0.932	1.005	1.094
gamma3_hat	100	0	1.000	0.031	0.921	1.002	1.072
theta_hat	100	0	0.332	0.081	0.139	0.331	0.558
theta_hat_t_stats	100	0	4.518	0.972	1.945	4.632	6.625
R2_demand	100	0	0.366	0.031	0.286	0.368	0.439
R2_supply	100	0	0.356	0.037	0.250	0.356	0.453

\(\alpha_2 = 1.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.881	0.911	7.719	9.780	12.297
alpha1_hat	100	0	0.820	3.832	−10.976	1.218	10.451
alpha2_hat	100	0	0.987	0.444	0.155	0.988	2.274
alpha3_hat	100	0	0.974	0.233	0.323	0.985	1.659
gamma0_hat	100	0	0.641	1.874	−6.248	0.962	3.918
gamma1_hat	100	0	−0.016	8.935	−31.752	0.069	59.196
gamma2_hat	100	0	1.053	0.269	0.550	1.019	1.986
gamma3_hat	100	0	1.061	0.272	0.609	1.016	2.385
theta_hat	100	0	0.545	0.970	−3.919	0.437	4.710
theta_hat_t_stats	100	0	0.756	0.912	−2.111	0.817	2.723
R2_demand	100	0	0.433	0.229	−0.605	0.487	0.756
R2_supply	100	0	0.349	0.329	−1.560	0.432	0.740

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.911	0.619	8.764	9.845	11.944
alpha1_hat	100	0	0.851	2.377	−4.596	0.806	6.231
alpha2_hat	100	0	0.991	0.288	0.353	0.978	1.800
alpha3_hat	100	0	0.999	0.152	0.641	0.992	1.480
gamma0_hat	100	0	0.931	0.933	−2.048	0.944	3.379
gamma1_hat	100	0	1.204	3.438	−6.497	1.582	9.392
gamma2_hat	100	0	1.011	0.142	0.694	0.998	1.433
gamma3_hat	100	0	0.996	0.146	0.687	0.990	1.483
theta_hat	100	0	0.333	0.356	−0.373	0.300	1.199
theta_hat_t_stats	100	0	0.980	0.965	−0.936	0.981	3.298
R2_demand	100	0	0.402	0.166	−0.199	0.436	0.642
R2_supply	100	0	0.393	0.157	−0.309	0.416	0.675

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.991	0.399	9.100	9.926	10.992
alpha1_hat	100	0	0.978	1.600	−2.596	1.086	4.918
alpha2_hat	100	0	1.004	0.184	0.606	0.988	1.468
alpha3_hat	100	0	0.998	0.087	0.807	0.986	1.228
gamma0_hat	100	0	1.030	0.696	−0.888	1.017	3.541
gamma1_hat	100	0	1.210	2.091	−6.672	1.261	6.603
gamma2_hat	100	0	0.990	0.104	0.637	0.987	1.256
gamma3_hat	100	0	0.998	0.100	0.708	0.998	1.296
theta_hat	100	0	0.311	0.221	−0.147	0.322	1.128
theta_hat_t_stats	100	0	1.407	0.889	−0.554	1.470	3.165
R2_demand	100	0	0.377	0.113	0.060	0.406	0.605
R2_supply	100	0	0.389	0.108	0.028	0.398	0.586

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.009	0.199	9.552	10.022	10.515
alpha1_hat	100	0	1.064	0.807	−1.336	1.050	3.026
alpha2_hat	100	0	0.997	0.092	0.774	0.993	1.273
alpha3_hat	100	0	1.006	0.052	0.901	1.006	1.140
gamma0_hat	100	0	1.004	0.274	0.250	0.994	1.552
gamma1_hat	100	0	0.893	0.917	−1.210	0.904	2.858
gamma2_hat	100	0	0.999	0.039	0.931	0.992	1.100
gamma3_hat	100	0	1.004	0.042	0.910	1.003	1.102
theta_hat	100	0	0.339	0.102	0.130	0.340	0.599
theta_hat_t_stats	100	0	3.622	0.928	1.590	3.607	5.669
R2_demand	100	0	0.392	0.048	0.264	0.393	0.500
R2_supply	100	0	0.395	0.047	0.273	0.396	0.486

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.983	0.130	9.671	9.990	10.252
alpha1_hat	100	0	1.070	0.629	−0.608	1.069	2.884
alpha2_hat	100	0	0.989	0.064	0.812	0.983	1.179
alpha3_hat	100	0	0.996	0.032	0.915	0.996	1.087
gamma0_hat	100	0	0.978	0.229	0.326	0.977	1.440
gamma1_hat	100	0	1.009	0.640	−0.480	1.067	2.528
gamma2_hat	100	0	1.002	0.034	0.939	1.000	1.092
gamma3_hat	100	0	1.002	0.038	0.935	0.997	1.104
theta_hat	100	0	0.335	0.065	0.178	0.330	0.476
theta_hat_t_stats	100	0	5.070	0.843	2.943	4.967	7.079
R2_demand	100	0	0.400	0.034	0.302	0.401	0.492
R2_supply	100	0	0.396	0.034	0.280	0.402	0.459

\(\alpha_2 = 5.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.155	1.110	8.022	9.940	14.074
alpha1_hat	100	0	−0.743	17.362	−47.100	−1.777	52.841
alpha2_hat	100	0	5.352	1.980	0.878	5.258	10.056
alpha3_hat	100	0	1.028	0.251	0.492	0.996	2.140
gamma0_hat	100	0	0.539	2.743	−15.815	1.036	3.283
gamma1_hat	100	0	2.477	22.916	−105.349	3.018	69.242
gamma2_hat	100	0	1.036	0.375	0.531	0.967	3.254
gamma3_hat	100	0	1.076	0.435	0.566	1.011	4.192
theta_hat	100	0	0.424	0.697	−0.752	0.225	4.011
theta_hat_t_stats	100	0	0.650	0.790	−1.640	0.623	2.371
R2_demand	100	0	0.344	0.381	−1.444	0.452	0.757
R2_supply	100	0	0.334	0.577	−3.722	0.456	0.785

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.034	0.656	8.761	9.962	12.255
alpha1_hat	100	0	1.650	12.396	−33.550	0.718	38.354
alpha2_hat	100	0	4.988	1.422	2.300	4.944	9.145
alpha3_hat	100	0	1.001	0.156	0.577	1.020	1.546
gamma0_hat	100	0	0.989	1.015	−1.669	1.226	2.975
gamma1_hat	100	0	−1.129	15.342	−40.129	−0.687	35.773
gamma2_hat	100	0	1.015	0.161	0.705	1.003	1.458
gamma3_hat	100	0	0.982	0.136	0.668	0.976	1.400
theta_hat	100	0	0.368	0.330	−0.324	0.357	1.578
theta_hat_t_stats	100	0	1.177	0.895	−1.420	1.283	2.479
R2_demand	100	0	0.424	0.158	−0.076	0.453	0.721
R2_supply	100	0	0.453	0.129	0.009	0.462	0.678

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.080	0.461	9.105	10.044	11.438
alpha1_hat	100	0	2.168	8.411	−18.957	2.191	21.653
alpha2_hat	100	0	4.968	0.909	2.360	4.973	7.329
alpha3_hat	100	0	1.003	0.094	0.807	0.992	1.269
gamma0_hat	100	0	0.991	0.655	−0.938	1.083	2.279
gamma1_hat	100	0	−1.505	9.800	−34.495	−1.450	22.510
gamma2_hat	100	0	0.996	0.101	0.776	0.982	1.237
gamma3_hat	100	0	1.000	0.100	0.813	0.998	1.248
theta_hat	100	0	0.381	0.241	−0.110	0.336	1.250
theta_hat_t_stats	100	0	1.849	0.899	−0.590	1.943	4.052
R2_demand	100	0	0.424	0.107	0.069	0.441	0.604
R2_supply	100	0	0.438	0.100	0.058	0.445	0.656

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.017	0.207	9.502	10.010	10.834
alpha1_hat	100	0	1.106	3.724	−11.821	0.780	11.378
alpha2_hat	100	0	5.009	0.401	4.036	5.032	6.438
alpha3_hat	100	0	0.998	0.050	0.890	1.000	1.130
gamma0_hat	100	0	0.964	0.330	0.185	0.961	1.600
gamma1_hat	100	0	0.862	4.285	−10.247	1.234	9.269
gamma2_hat	100	0	1.004	0.052	0.881	0.999	1.128
gamma3_hat	100	0	1.000	0.045	0.885	1.000	1.095
theta_hat	100	0	0.338	0.095	0.096	0.328	0.580
theta_hat_t_stats	100	0	3.998	0.955	1.308	4.038	6.275
R2_demand	100	0	0.435	0.049	0.297	0.443	0.561
R2_supply	100	0	0.430	0.044	0.272	0.431	0.512

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.998	0.146	9.661	10.001	10.377
alpha1_hat	100	0	0.880	2.928	−9.563	0.832	8.123
alpha2_hat	100	0	5.011	0.310	4.243	5.014	6.091
alpha3_hat	100	0	0.998	0.030	0.908	0.999	1.086
gamma0_hat	100	0	1.014	0.230	0.491	1.038	1.523
gamma1_hat	100	0	0.887	2.866	−7.982	0.992	7.093
gamma2_hat	100	0	0.999	0.034	0.902	1.004	1.083
gamma3_hat	100	0	0.999	0.032	0.934	0.995	1.096
theta_hat	100	0	0.330	0.069	0.186	0.322	0.474
theta_hat_t_stats	100	0	5.620	0.949	3.367	5.567	7.275
R2_demand	100	0	0.437	0.032	0.337	0.438	0.501
R2_supply	100	0	0.442	0.033	0.356	0.441	0.522

\(\alpha_2 = 20.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.012	1.402	7.889	9.766	20.673
alpha1_hat	100	0	7.425	85.038	−130.833	7.690	601.521
alpha2_hat	100	0	19.400	7.157	3.583	18.262	41.696
alpha3_hat	100	0	1.006	0.267	0.477	0.984	2.735
gamma0_hat	100	0	0.855	1.443	−3.955	0.769	4.436
gamma1_hat	100	0	−27.478	100.281	−423.172	−8.324	164.203
gamma2_hat	100	0	1.021	0.218	0.473	1.035	1.712
gamma3_hat	100	0	1.045	0.215	0.485	1.019	1.618
theta_hat	100	0	0.507	0.610	−0.570	0.374	3.227
theta_hat_t_stats	100	0	0.880	0.818	−1.123	0.917	2.508
R2_demand	100	0	0.371	0.875	−7.955	0.533	0.791
R2_supply	100	0	0.437	0.204	−0.273	0.474	0.745

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.079	0.710	8.357	9.956	13.374
alpha1_hat	100	0	−5.827	50.208	−119.702	1.818	123.228
alpha2_hat	100	0	20.975	6.353	4.808	19.588	36.780
alpha3_hat	100	0	1.019	0.150	0.700	0.997	1.424
gamma0_hat	100	0	0.844	1.080	−2.479	0.841	2.832
gamma1_hat	100	0	−1.076	73.058	−309.002	5.744	216.125
gamma2_hat	100	0	1.035	0.164	0.622	1.004	1.578
gamma3_hat	100	0	1.001	0.159	0.653	0.989	1.507
theta_hat	100	0	0.370	0.455	−0.590	0.262	2.811
theta_hat_t_stats	100	0	1.149	0.941	−1.432	1.189	4.282
R2_demand	100	0	0.415	0.203	−0.875	0.450	0.720
R2_supply	100	0	0.441	0.141	0.018	0.456	0.709

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.922	0.407	9.079	9.935	10.884
alpha1_hat	100	0	−1.508	28.924	−68.330	−3.907	68.355
alpha2_hat	100	0	19.881	3.396	11.564	19.740	28.292
alpha3_hat	100	0	0.982	0.101	0.768	0.984	1.289
gamma0_hat	100	0	0.963	0.740	−1.027	1.044	2.517
gamma1_hat	100	0	3.467	39.149	−95.363	5.773	124.265
gamma2_hat	100	0	1.001	0.107	0.722	0.993	1.323
gamma3_hat	100	0	1.007	0.115	0.692	1.011	1.284
theta_hat	100	0	0.335	0.224	−0.319	0.307	1.260
theta_hat_t_stats	100	0	1.666	0.957	−1.529	1.725	3.495
R2_demand	100	0	0.446	0.109	0.103	0.464	0.666
R2_supply	100	0	0.426	0.103	0.191	0.448	0.633

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.014	0.213	9.553	10.005	10.726
alpha1_hat	100	0	−0.823	13.567	−28.407	−2.822	40.858
alpha2_hat	100	0	20.238	1.701	16.009	20.199	24.180
alpha3_hat	100	0	1.003	0.048	0.920	1.002	1.161
gamma0_hat	100	0	0.996	0.287	0.179	1.020	1.546
gamma1_hat	100	0	0.838	15.014	−52.139	2.099	33.161
gamma2_hat	100	0	1.000	0.046	0.914	1.001	1.111
gamma3_hat	100	0	1.009	0.043	0.914	1.004	1.135
theta_hat	100	0	0.332	0.085	0.141	0.328	0.651
theta_hat_t_stats	100	0	4.049	0.869	2.059	3.945	6.470
R2_demand	100	0	0.450	0.053	0.302	0.458	0.542
R2_supply	100	0	0.448	0.041	0.339	0.452	0.536

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.988	0.137	9.717	9.973	10.406
alpha1_hat	100	0	1.148	10.368	−31.475	0.356	30.391
alpha2_hat	100	0	19.959	1.206	17.236	19.892	23.249
alpha3_hat	100	0	0.999	0.031	0.925	0.999	1.086
gamma0_hat	100	0	0.963	0.199	0.531	0.942	1.557
gamma1_hat	100	0	1.428	9.773	−22.716	1.421	22.038
gamma2_hat	100	0	1.004	0.028	0.907	1.002	1.069
gamma3_hat	100	0	1.001	0.033	0.920	1.001	1.070
theta_hat	100	0	0.334	0.057	0.212	0.335	0.480
theta_hat_t_stats	100	0	5.750	0.827	4.022	5.721	7.626
R2_demand	100	0	0.446	0.035	0.350	0.447	0.527
R2_supply	100	0	0.443	0.030	0.353	0.438	0.521

\(\theta = 0.5\)

\(\alpha_2 = 0.1\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.068	1.045	7.915	9.982	13.936
alpha1_hat	100	0	1.002	1.373	−1.912	1.049	7.658
alpha2_hat	100	0	0.104	0.129	−0.276	0.093	0.585
alpha3_hat	100	0	0.987	0.208	0.523	0.976	1.566
gamma0_hat	100	0	0.738	2.124	−9.781	1.169	3.994
gamma1_hat	100	0	3.745	27.350	−15.803	1.268	265.584
gamma2_hat	100	0	1.013	0.253	0.454	0.956	1.860
gamma3_hat	100	0	1.032	0.233	0.498	1.021	1.832
theta_hat	100	0	−0.371	11.123	−104.077	0.420	13.239
theta_hat_t_stats	100	0	0.380	1.033	−2.757	0.571	2.346
R2_demand	100	0	0.125	0.446	−2.641	0.237	0.556
R2_supply	100	0	0.054	0.956	−7.897	0.270	0.619

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.942	0.620	8.837	9.822	12.284
alpha1_hat	100	0	1.077	0.863	−0.684	1.102	5.283
alpha2_hat	100	0	0.089	0.076	−0.161	0.093	0.261
alpha3_hat	100	0	0.994	0.148	0.680	0.990	1.396
gamma0_hat	100	0	0.998	1.121	−2.465	1.236	2.971
gamma1_hat	100	0	0.563	4.488	−26.166	0.846	17.330
gamma2_hat	100	0	0.996	0.170	0.620	1.001	1.466
gamma3_hat	100	0	1.008	0.139	0.745	1.000	1.398
theta_hat	100	0	0.757	2.486	−11.887	0.633	14.242
theta_hat_t_stats	100	0	0.679	1.047	−2.177	0.649	3.384
R2_demand	100	0	0.200	0.209	−0.678	0.235	0.613
R2_supply	100	0	0.196	0.257	−0.857	0.265	0.540

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.972	0.468	8.912	9.949	10.966
alpha1_hat	100	0	0.955	0.510	−0.215	0.908	2.705
alpha2_hat	100	0	0.102	0.050	−0.020	0.098	0.219
alpha3_hat	100	0	0.983	0.101	0.773	0.981	1.267
gamma0_hat	100	0	0.951	0.743	−2.020	1.069	2.575
gamma1_hat	100	0	0.952	2.608	−10.691	0.876	19.690
gamma2_hat	100	0	1.006	0.110	0.716	0.992	1.472
gamma3_hat	100	0	1.007	0.098	0.798	1.009	1.298
theta_hat	100	0	0.560	1.561	−10.086	0.565	9.036
theta_hat_t_stats	100	0	1.021	1.023	−2.788	1.057	3.733
R2_demand	100	0	0.188	0.151	−0.202	0.204	0.447
R2_supply	100	0	0.171	0.187	−0.831	0.196	0.525

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.992	0.197	9.598	9.982	10.443
alpha1_hat	100	0	0.975	0.235	0.360	0.962	1.452
alpha2_hat	100	0	0.102	0.023	0.059	0.100	0.187
alpha3_hat	100	0	1.001	0.046	0.915	0.997	1.101
gamma0_hat	100	0	1.039	0.304	0.188	1.046	1.789
gamma1_hat	100	0	1.062	0.491	−0.258	1.052	2.196
gamma2_hat	100	0	0.997	0.045	0.897	0.998	1.134
gamma3_hat	100	0	0.993	0.049	0.880	0.995	1.139
theta_hat	100	0	0.462	0.262	−0.104	0.443	1.152
theta_hat_t_stats	100	0	2.045	1.003	−0.543	2.065	3.956
R2_demand	100	0	0.195	0.066	0.021	0.200	0.320
R2_supply	100	0	0.209	0.054	0.063	0.215	0.345

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.008	0.139	9.666	10.013	10.278
alpha1_hat	100	0	0.995	0.176	0.583	0.985	1.451
alpha2_hat	100	0	0.101	0.017	0.064	0.102	0.144
alpha3_hat	100	0	1.005	0.030	0.930	1.005	1.080
gamma0_hat	100	0	0.971	0.218	0.494	0.981	1.460
gamma1_hat	100	0	0.942	0.341	−0.036	0.998	1.505
gamma2_hat	100	0	1.004	0.034	0.932	1.003	1.078
gamma3_hat	100	0	1.001	0.031	0.933	1.000	1.105
theta_hat	100	0	0.533	0.171	0.211	0.507	0.969
theta_hat_t_stats	100	0	3.396	0.832	1.488	3.371	5.278
R2_demand	100	0	0.202	0.041	0.083	0.205	0.277
R2_supply	100	0	0.200	0.039	0.106	0.202	0.287

\(\alpha_2 = 0.5\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.918	1.030	7.960	9.700	14.079
alpha1_hat	100	0	0.635	2.503	−4.577	0.383	7.811
alpha2_hat	100	0	0.522	0.295	−0.166	0.537	1.309
alpha3_hat	100	0	0.993	0.217	0.623	0.971	1.780
gamma0_hat	100	0	0.330	1.867	−7.538	0.554	3.598
gamma1_hat	100	0	−3.952	43.802	−412.503	1.299	40.828
gamma2_hat	100	0	1.066	0.258	0.526	1.025	1.782
gamma3_hat	100	0	1.056	0.285	0.593	0.997	2.381
theta_hat	100	0	1.763	9.830	−6.911	0.527	95.646
theta_hat_t_stats	100	0	0.822	0.981	−2.637	0.863	3.001
R2_demand	100	0	0.262	0.375	−1.820	0.348	0.696
R2_supply	100	0	0.151	0.427	−2.232	0.243	0.654

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.042	0.710	8.658	9.920	12.798
alpha1_hat	100	0	1.142	1.940	−3.704	0.923	7.108
alpha2_hat	100	0	0.494	0.197	−0.054	0.486	1.028
alpha3_hat	100	0	1.019	0.154	0.644	1.032	1.481
gamma0_hat	100	0	1.102	1.004	−1.346	1.185	3.312
gamma1_hat	100	0	0.687	6.103	−21.565	1.301	41.843
gamma2_hat	100	0	0.993	0.147	0.644	0.981	1.395
gamma3_hat	100	0	0.989	0.140	0.699	1.000	1.514
theta_hat	100	0	0.549	1.016	−5.737	0.387	3.951
theta_hat_t_stats	100	0	1.127	0.960	−1.718	1.152	2.974
R2_demand	100	0	0.260	0.243	−1.117	0.336	0.554
R2_supply	100	0	0.297	0.186	−0.250	0.326	0.590

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.008	0.452	9.236	9.951	11.002
alpha1_hat	100	0	0.901	1.288	−2.563	0.945	4.009
alpha2_hat	100	0	0.511	0.126	0.169	0.517	0.786
alpha3_hat	100	0	0.992	0.093	0.735	0.992	1.356
gamma0_hat	100	0	1.006	0.654	−0.650	0.996	2.533
gamma1_hat	100	0	0.888	1.891	−8.429	0.982	6.502
gamma2_hat	100	0	0.997	0.101	0.789	0.992	1.328
gamma3_hat	100	0	0.993	0.107	0.778	0.981	1.295
theta_hat	100	0	0.526	0.355	−0.233	0.480	2.127
theta_hat_t_stats	100	0	1.860	0.876	−0.426	1.991	3.695
R2_demand	100	0	0.270	0.137	−0.168	0.277	0.526
R2_supply	100	0	0.275	0.112	−0.067	0.288	0.537

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.985	0.190	9.511	9.980	10.607
alpha1_hat	100	0	1.057	0.577	−0.562	1.106	2.106
alpha2_hat	100	0	0.492	0.063	0.370	0.482	0.652
alpha3_hat	100	0	0.997	0.045	0.884	0.996	1.102
gamma0_hat	100	0	0.982	0.338	−0.035	1.001	2.124
gamma1_hat	100	0	0.902	0.769	−0.901	0.913	2.540
gamma2_hat	100	0	1.001	0.050	0.801	1.000	1.140
gamma3_hat	100	0	1.003	0.046	0.873	0.999	1.142
theta_hat	100	0	0.524	0.125	0.268	0.531	0.880
theta_hat_t_stats	100	0	4.388	0.892	2.378	4.412	6.896
R2_demand	100	0	0.292	0.056	0.164	0.300	0.415
R2_supply	100	0	0.285	0.055	0.079	0.284	0.403

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.997	0.154	9.672	9.988	10.373
alpha1_hat	100	0	0.951	0.370	0.116	0.988	2.276
alpha2_hat	100	0	0.505	0.040	0.409	0.505	0.618
alpha3_hat	100	0	1.001	0.034	0.914	0.997	1.070
gamma0_hat	100	0	0.964	0.232	0.407	0.968	1.403
gamma1_hat	100	0	1.000	0.510	−0.121	0.996	2.040
gamma2_hat	100	0	1.005	0.035	0.936	1.008	1.084
gamma3_hat	100	0	1.004	0.036	0.907	1.003	1.092
theta_hat	100	0	0.507	0.091	0.315	0.521	0.694
theta_hat_t_stats	100	0	6.240	0.928	4.305	6.243	8.591
R2_demand	100	0	0.286	0.046	0.149	0.289	0.386
R2_supply	100	0	0.283	0.037	0.175	0.283	0.361

\(\alpha_2 = 1.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.025	1.054	8.416	9.819	13.799
alpha1_hat	100	0	1.174	4.966	−12.688	0.825	25.156
alpha2_hat	100	0	0.989	0.588	−0.632	0.949	2.952
alpha3_hat	100	0	1.004	0.258	0.489	0.952	1.923
gamma0_hat	100	0	0.814	1.716	−9.207	0.869	4.640
gamma1_hat	100	0	−3.798	28.528	−259.759	2.076	17.332
gamma2_hat	100	0	1.034	0.225	0.592	1.059	2.011
gamma3_hat	100	0	1.009	0.230	0.473	1.016	1.900
theta_hat	100	0	1.090	3.228	−1.121	0.344	30.113
theta_hat_t_stats	100	0	0.864	0.940	−1.943	0.946	3.401
R2_demand	100	0	0.275	0.424	−2.122	0.397	0.744
R2_supply	100	0	0.306	0.345	−2.229	0.362	0.736

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.014	0.683	8.583	9.864	12.234
alpha1_hat	100	0	0.899	2.964	−7.428	0.718	8.488
alpha2_hat	100	0	1.017	0.314	0.322	1.005	2.141
alpha3_hat	100	0	0.993	0.136	0.714	0.979	1.387
gamma0_hat	100	0	0.880	0.947	−2.870	0.853	2.937
gamma1_hat	100	0	0.723	4.365	−14.154	1.815	9.577
gamma2_hat	100	0	1.019	0.142	0.696	1.016	1.576
gamma3_hat	100	0	1.008	0.136	0.677	0.994	1.416
theta_hat	100	0	0.542	0.431	−0.306	0.429	2.409
theta_hat_t_stats	100	0	1.448	0.846	−0.844	1.372	3.426
R2_demand	100	0	0.304	0.191	−0.249	0.329	0.608
R2_supply	100	0	0.329	0.162	−0.256	0.362	0.623

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.052	0.488	8.847	10.022	11.306
alpha1_hat	100	0	1.198	2.177	−3.931	1.367	6.972
alpha2_hat	100	0	0.993	0.241	0.512	0.976	1.761
alpha3_hat	100	0	1.016	0.106	0.780	1.002	1.317
gamma0_hat	100	0	0.862	0.718	−2.439	0.947	2.256
gamma1_hat	100	0	0.604	2.878	−7.175	1.118	6.459
gamma2_hat	100	0	1.011	0.102	0.800	0.993	1.481
gamma3_hat	100	0	1.015	0.098	0.820	0.999	1.366
theta_hat	100	0	0.571	0.309	−0.035	0.516	1.487
theta_hat_t_stats	100	0	2.176	0.873	−0.160	2.116	4.171
R2_demand	100	0	0.293	0.138	−0.167	0.305	0.528
R2_supply	100	0	0.294	0.156	−0.291	0.313	0.585

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.032	0.204	9.599	10.041	10.669
alpha1_hat	100	0	1.042	0.942	−1.293	1.059	3.488
alpha2_hat	100	0	1.005	0.111	0.657	1.021	1.303
alpha3_hat	100	0	1.004	0.041	0.910	1.006	1.118
gamma0_hat	100	0	0.930	0.343	0.017	0.994	1.878
gamma1_hat	100	0	1.012	1.121	−1.948	1.030	4.781
gamma2_hat	100	0	1.006	0.052	0.900	0.999	1.138
gamma3_hat	100	0	1.007	0.041	0.875	1.007	1.106
theta_hat	100	0	0.510	0.120	0.157	0.505	0.916
theta_hat_t_stats	100	0	4.850	0.867	1.761	4.874	6.715
R2_demand	100	0	0.313	0.053	0.145	0.312	0.413
R2_supply	100	0	0.301	0.061	0.114	0.305	0.434

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.032	0.154	9.640	10.025	10.500
alpha1_hat	100	0	1.070	0.659	−0.595	0.976	2.432
alpha2_hat	100	0	1.003	0.079	0.770	1.007	1.191
alpha3_hat	100	0	1.005	0.031	0.933	1.000	1.081
gamma0_hat	100	0	0.959	0.243	0.362	0.964	1.572
gamma1_hat	100	0	1.038	0.850	−1.009	1.011	3.044
gamma2_hat	100	0	1.008	0.034	0.924	1.006	1.079
gamma3_hat	100	0	1.004	0.031	0.916	1.004	1.088
theta_hat	100	0	0.498	0.081	0.262	0.494	0.674
theta_hat_t_stats	100	0	6.805	0.913	4.385	6.800	9.071
R2_demand	100	0	0.313	0.042	0.214	0.318	0.400
R2_supply	100	0	0.318	0.041	0.226	0.317	0.417

\(\alpha_2 = 5.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.905	0.857	7.903	9.839	13.046
alpha1_hat	100	0	1.229	19.905	−56.477	−1.308	46.467
alpha2_hat	100	0	4.838	2.291	−0.843	5.057	11.967
alpha3_hat	100	0	0.994	0.178	0.653	0.978	1.503
gamma0_hat	100	0	0.737	1.491	−4.036	1.038	3.492
gamma1_hat	100	0	−5.312	160.588	−817.729	−0.157	1227.512
gamma2_hat	100	0	1.031	0.235	0.594	0.993	1.703
gamma3_hat	100	0	1.046	0.223	0.616	1.027	1.849
theta_hat	100	0	0.649	4.575	−36.293	0.580	20.544
theta_hat_t_stats	100	0	1.087	0.931	−2.335	1.315	2.911
R2_demand	100	0	0.355	0.287	−1.042	0.408	0.736
R2_supply	100	0	0.350	0.223	−0.321	0.408	0.743

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.060	0.675	8.425	10.004	12.044
alpha1_hat	100	0	0.282	13.587	−33.200	−1.095	43.051
alpha2_hat	100	0	5.147	1.474	0.676	5.129	9.030
alpha3_hat	100	0	0.999	0.156	0.745	0.993	1.553
gamma0_hat	100	0	0.844	1.140	−2.899	1.024	2.943
gamma1_hat	100	0	0.865	26.412	−216.314	3.537	34.904
gamma2_hat	100	0	1.012	0.164	0.663	0.998	1.461
gamma3_hat	100	0	1.014	0.162	0.692	1.028	1.501
theta_hat	100	0	0.549	0.553	−0.152	0.444	4.770
theta_hat_t_stats	100	0	1.443	0.743	−0.614	1.499	2.981
R2_demand	100	0	0.312	0.260	−0.988	0.370	0.586
R2_supply	100	0	0.293	0.237	−1.082	0.342	0.601

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.960	0.473	8.789	9.966	11.243
alpha1_hat	100	0	−0.095	9.647	−19.686	0.279	20.684
alpha2_hat	100	0	5.058	1.106	2.841	4.852	8.631
alpha3_hat	100	0	0.994	0.114	0.770	0.985	1.251
gamma0_hat	100	0	0.880	0.783	−2.403	0.970	2.485
gamma1_hat	100	0	0.108	12.032	−39.482	0.970	26.673
gamma2_hat	100	0	1.010	0.117	0.754	1.012	1.428
gamma3_hat	100	0	1.014	0.124	0.776	0.992	1.414
theta_hat	100	0	0.552	0.268	−0.004	0.518	1.557
theta_hat_t_stats	100	0	2.441	0.876	−0.022	2.376	4.325
R2_demand	100	0	0.342	0.130	−0.090	0.361	0.561
R2_supply	100	0	0.324	0.141	−0.306	0.333	0.580

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.016	0.184	9.555	10.003	10.435
alpha1_hat	100	0	1.571	3.895	−7.121	1.534	10.478
alpha2_hat	100	0	4.965	0.453	3.772	4.948	5.792
alpha3_hat	100	0	1.003	0.043	0.913	1.002	1.110
gamma0_hat	100	0	1.013	0.281	0.181	0.998	1.616
gamma1_hat	100	0	0.285	4.807	−9.959	0.197	11.288
gamma2_hat	100	0	0.999	0.040	0.905	1.003	1.133
gamma3_hat	100	0	0.994	0.044	0.886	0.990	1.122
theta_hat	100	0	0.511	0.099	0.243	0.515	0.698
theta_hat_t_stats	100	0	5.378	0.876	3.201	5.441	7.254
R2_demand	100	0	0.341	0.053	0.182	0.347	0.431
R2_supply	100	0	0.353	0.050	0.219	0.361	0.474

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.005	0.139	9.680	10.007	10.451
alpha1_hat	100	0	1.166	2.547	−3.731	0.902	6.745
alpha2_hat	100	0	4.994	0.341	4.223	5.031	5.811
alpha3_hat	100	0	1.004	0.034	0.927	1.005	1.089
gamma0_hat	100	0	1.003	0.201	0.508	1.017	1.605
gamma1_hat	100	0	0.523	3.522	−11.355	0.797	9.824
gamma2_hat	100	0	0.999	0.028	0.905	0.997	1.072
gamma3_hat	100	0	0.998	0.029	0.883	1.000	1.047
theta_hat	100	0	0.509	0.084	0.293	0.506	0.722
theta_hat_t_stats	100	0	7.599	0.987	4.524	7.715	10.192
R2_demand	100	0	0.344	0.042	0.237	0.346	0.452
R2_supply	100	0	0.345	0.034	0.254	0.345	0.406

\(\alpha_2 = 20.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.952	1.012	8.115	9.864	13.583
alpha1_hat	100	0	−6.081	81.140	−175.858	−5.806	224.524
alpha2_hat	100	0	20.447	8.570	−2.178	20.765	39.275
alpha3_hat	100	0	0.966	0.235	0.550	0.939	1.762
gamma0_hat	100	0	0.839	1.760	−7.683	1.029	4.745
gamma1_hat	100	0	−209.454	1634.353	−16118.530	−2.292	213.426
gamma2_hat	100	0	1.024	0.252	0.573	1.000	2.014
gamma3_hat	100	0	1.041	0.246	0.507	1.020	1.782
theta_hat	100	0	1.795	9.343	−0.650	0.528	92.086
theta_hat_t_stats	100	0	1.147	0.959	−1.824	1.186	3.131
R2_demand	100	0	0.319	0.389	−1.852	0.434	0.806
R2_supply	100	0	0.316	0.432	−2.774	0.401	0.748

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.919	0.624	8.551	9.892	12.815
alpha1_hat	100	0	3.180	50.544	−105.249	3.688	130.740
alpha2_hat	100	0	19.360	6.359	5.189	18.479	43.643
alpha3_hat	100	0	1.000	0.152	0.649	0.982	1.449
gamma0_hat	100	0	1.025	0.794	−0.906	1.065	3.289
gamma1_hat	100	0	−13.671	68.100	−233.919	−0.987	132.235
gamma2_hat	100	0	1.000	0.125	0.665	0.995	1.288
gamma3_hat	100	0	0.995	0.142	0.656	0.976	1.316
theta_hat	100	0	0.599	0.411	−0.114	0.550	2.040
theta_hat_t_stats	100	0	1.672	0.864	−0.411	1.635	3.555
R2_demand	100	0	0.351	0.274	−1.872	0.380	0.676
R2_supply	100	0	0.356	0.144	−0.077	0.350	0.668

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.013	0.473	8.633	9.987	11.164
alpha1_hat	100	0	0.905	38.348	−127.127	7.208	71.531
alpha2_hat	100	0	20.126	4.806	9.769	19.467	38.683
alpha3_hat	100	0	1.013	0.100	0.800	1.018	1.314
gamma0_hat	100	0	0.966	0.730	−2.368	1.007	2.269
gamma1_hat	100	0	−5.638	39.944	−115.338	0.932	78.109
gamma2_hat	100	0	0.995	0.109	0.738	0.993	1.296
gamma3_hat	100	0	1.007	0.112	0.767	1.010	1.450
theta_hat	100	0	0.557	0.275	0.022	0.550	1.717
theta_hat_t_stats	100	0	2.454	0.875	0.119	2.507	4.810
R2_demand	100	0	0.326	0.140	−0.064	0.359	0.547
R2_supply	100	0	0.346	0.124	−0.145	0.363	0.584

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.992	0.192	9.555	9.974	10.513
alpha1_hat	100	0	2.092	14.772	−39.193	3.266	45.123
alpha2_hat	100	0	19.835	1.710	14.689	19.769	23.925
alpha3_hat	100	0	1.002	0.042	0.916	0.996	1.100
gamma0_hat	100	0	1.012	0.291	0.075	0.997	1.996
gamma1_hat	100	0	2.384	16.937	−40.210	2.903	41.254
gamma2_hat	100	0	0.997	0.044	0.879	1.000	1.134
gamma3_hat	100	0	1.004	0.048	0.911	1.003	1.147
theta_hat	100	0	0.494	0.096	0.264	0.503	0.706
theta_hat_t_stats	100	0	5.299	0.847	3.097	5.434	7.016
R2_demand	100	0	0.356	0.048	0.230	0.362	0.464
R2_supply	100	0	0.357	0.042	0.248	0.358	0.449

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.992	0.192	9.555	9.974	10.513
alpha1_hat	100	0	2.092	14.772	−39.193	3.266	45.123
alpha2_hat	100	0	19.835	1.710	14.689	19.769	23.925
alpha3_hat	100	0	1.002	0.042	0.916	0.996	1.100
gamma0_hat	100	0	1.012	0.291	0.075	0.997	1.996
gamma1_hat	100	0	2.384	16.937	−40.210	2.903	41.254
gamma2_hat	100	0	0.997	0.044	0.879	1.000	1.134
gamma3_hat	100	0	1.004	0.048	0.911	1.003	1.147
theta_hat	100	0	0.494	0.096	0.264	0.503	0.706
theta_hat_t_stats	100	0	5.299	0.847	3.097	5.434	7.016
R2_demand	100	0	0.356	0.048	0.230	0.362	0.464
R2_supply	100	0	0.357	0.042	0.248	0.358	0.449